{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Black Scholes valuation methods\n",
    "\n",
    "[*Black Scholes model WIKI*](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model). \n",
    "\n",
    "\n",
    "The purpose of this notebook is to review the most common algorithms and implement them numerically. \n",
    "\n",
    "## Contents\n",
    "   - [European option](#sec1)\n",
    "      - [Put-Call parity](#sec1.1)\n",
    "   - [Numerical integration](#sec2)\n",
    "   - [Monte Carlo method](#sec3)\n",
    "   - [Binomial tree](#sec4)\n",
    "   - [Limits of the model](#sec5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from FMNM.BS_pricer import BS_pricer\n",
    "from FMNM.Parameters import Option_param\n",
    "from FMNM.Processes import Diffusion_process\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as ss\n",
    "from scipy.integrate import quad\n",
    "from functools import partial\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "## European option\n",
    "\n",
    "Under the Black-Scholes (BS) model, the best method to price a vanilla European option is to use the [BS closed formula](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model).\n",
    "\n",
    "The **BS formula** for a call is:\n",
    "\n",
    "$$ C(t,T,S,K,r,\\sigma) = S \\, N(d_1) - K e^{-r(T-t)} N(d_2) $$\n",
    "\n",
    "with \n",
    "\n",
    "$$ d_1 = \\frac{1}{\\sigma \\sqrt{T-t}} \\biggl[ \\log \\biggl( \\frac{S}{K} \\biggr) + \\biggl(r + \\frac{\\sigma^2}{2} \\biggr) (T-t) \\biggr] \\quad \\text{and} \\quad d_2 = d_1 - \\sigma \\sqrt{T-t} $$\n",
    "\n",
    "where $N$ is the cumulative distribution function of a standard normal random variable.    \n",
    "The formula for a put is similar and can be found in the wiki page.\n",
    "\n",
    "The value of an option can be also computed as the discounted expectation of a future payoff in this way:\n",
    "\n",
    "$$\\begin{aligned}\n",
    " C(s,K,t, T) &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_t=s \\biggr] \\\\\n",
    "            &= e^{-r(T-t)} \\int_0^{\\infty}\\, (s' - K)^+ \\, f(s'|s) \\, ds' \\\\\n",
    "            &= e^{-r(T-t)} \\int_K^{\\infty}\\, (s' - K) \\, f(s'|s) \\, ds' \n",
    "\\end{aligned}$$\n",
    "\n",
    "where $f(s'|s)$ is the risk neutral transition probability of the process $\\{S_u\\}_{u\\in [t,T]}$ starting at $S_t=s$. This is a log-normal density function \n",
    "\n",
    "$$ f(s'|s) = \\frac{1}{s' \\sigma \\sqrt{2\\pi (T-t)}} \\; e^{- \\frac{ \\biggl[\\log(s') - \\bigl(\\log(s) + (r-\\frac{1}{2} \\sigma^2)(T-t) \\bigr) \\biggr]^2}{2\\sigma^2 (T-t)}} $$\n",
    "\n",
    "\n",
    "#### Comment:\n",
    "Usually in statistics random variables are indicated by capital letters, and non-random variables are indicated with small letters. However, it is very common to indicate the stock price in the Black-Scholes formula with a capital letter e.g [wiki notation](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Notation). I'm going to use a capital letters to indicate random variables, and small letters for non random. However there will be exceptions where it will be clear from the context e.g. strike K and maturity T are non random, or $S_0$ most of the time is a fixed variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let us analyze better the previous formulas\n",
    "\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    " C(s,t,K,T) &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_t=s \\biggr] \\\\\n",
    "            &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \n",
    "              - e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ K \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \\\\\n",
    "            &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \n",
    "              - e^{-r(T-t)} K \\, \\underbrace{\\mathbb{Q}\\biggl[ S_T >K \\bigg| S_t=s \\biggr]}_{N(d_2)} \\\\            \n",
    "\\end{align*}\n",
    "\n",
    "Let us introduce the following change of measure (under the stock numeraire):\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "\\frac{d \\tilde{\\mathbb{Q}} }{ d \\mathbb{Q} } &= \\frac{S_T}{\\mathbb{E}^\\mathbb{Q}[S_T | S_t]} = \\frac{S_T}{S_t e^{r(T-t)}}  \\\\ \n",
    "                                            &= \\frac{S_t e^{(r -\\frac{1}{2}\\sigma^2)(T-t) + \\sigma W_{T-t}} }{S_t e^{r(T-t)}} \\\\\n",
    "                                            &=   e^{ -\\frac{1}{2}\\sigma^2(T-t) + \\sigma W_{T-t} } \\quad \\text{(exponential martingale)} \n",
    "\\end{aligned} $$\n",
    "\n",
    "By [Girsanov theorem](https://en.wikipedia.org/wiki/Girsanov_theorem), under $\\tilde{\\mathbb{Q}}$ the driving Brownian motion has the new dynamics \n",
    "\n",
    "$$ \\tilde{W_t} = W_t - \\sigma t $$\n",
    "\n",
    "and the corresponding stock dynamics becomes\n",
    "\n",
    "$$\\begin{aligned}\n",
    " \\frac{dS_t}{S_t} &= r dt + \\sigma dW_t \\\\\n",
    "                  &= (r+\\sigma^2) dt + \\sigma d\\tilde{W}_t \n",
    "\\end{aligned}$$\n",
    "\n",
    "The first term is\n",
    "\n",
    "$$ \\begin{aligned}\n",
    " e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] =& e^{-r(T-t)} \\mathbb{E}^{\\tilde{\\mathbb{Q}}} \n",
    "                 \\biggl[ \\frac{d \\mathbb{Q} }{ d \\tilde{\\mathbb{Q}}}  S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \\\\\n",
    "                     =& e^{-r(T-t)} \\mathbb{E}^{\\tilde{\\mathbb{Q}}} \n",
    "                 \\biggl[ \\frac{e^{r(T-t)}S_t}{S_T}  S_T \\mathbb{1}_{S_T > K} \\bigg| S_t=s \\biggr] \\\\ \n",
    "                    =& \\; s \\, \\underbrace{\\tilde{\\mathbb{Q}} ( S_T > K | S_t=s)}_{N(d_1)}\n",
    "\\end{aligned}$$\n",
    "\n",
    "We have just seen how to interpret the terms $N(d_1)$ and $N(d_2)$. These are the risk neutral probabilities of $S_T > K$ in the stock and money market numeraires respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I implemented the BS closed formula in the class `BS_pricer`.     \n",
    "Let us consider the following set of parameters, that will be recurrent in all the next notebooks. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 100.0  # spot stock price\n",
    "K = 100.0  # strike\n",
    "T = 1.0  # maturity\n",
    "r = 0.1  # risk free rate\n",
    "sig = 0.2  # diffusion coefficient or volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call price:  13.269676584660893\n",
      "Put price:  3.753418388256833\n"
     ]
    }
   ],
   "source": [
    "call = BS_pricer.BlackScholes(\"call\", S0, K, T, r, sig)\n",
    "put = BS_pricer.BlackScholes(\"put\", S0, K, T, r, sig)\n",
    "print(\"Call price: \", call)\n",
    "print(\"Put price: \", put)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.1'></a>\n",
    "### Put-Call parity\n",
    "\n",
    "This is an important formula [wiki page](https://en.wikipedia.org/wiki/Put%E2%80%93call_parity)\n",
    "\n",
    "$$ Call - Put = S_0 - K e^{-rT}  $$\n",
    "\n",
    "Let us check if it works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.269676584660893\n",
      "13.269676584660886\n"
     ]
    }
   ],
   "source": [
    "print(call)\n",
    "print(put + S0 - K * np.exp(-r * T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "## Numerical integration\n",
    "\n",
    "I want to play a bit with the different formulas written above.  \n",
    "\n",
    "Let us compute the option prices by integrating the log-normal density:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_ret = np.log(S0) + (r - 0.5 * sig**2) * T  # expected return of the log-price\n",
    "vol = sig * np.sqrt(T)  # standard deviation of the log-price\n",
    "\n",
    "\n",
    "# log-normal density (defined above)\n",
    "def log_normal(x, e_ret, vol):\n",
    "    return 1 / (x * vol * np.sqrt(2 * np.pi)) * np.exp(-((np.log(x) - e_ret) ** 2) / (2 * vol**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 5))\n",
    "x = np.linspace(30, 190, 100)\n",
    "plt.plot(x, log_normal(x, e_ret, vol))\n",
    "plt.title(\"Lognormal distribution, conditioned on $S_0=100$\")\n",
    "plt.xlabel(\"$S_T$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `log_normal(x, e_ret, vol)` defined above, corresponds to the scipy.stats function: \n",
    "```\n",
    "ss.lognorm.pdf(x, vol, scale=np.exp(e_ret) ).\n",
    "```\n",
    "\n",
    "In the next calculation, I'm going to use the scipy function.    \n",
    "Let us perform the integration with the `scipy.integrate` function [quad](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call price: 13.269676584660926 \n",
      "Put price: 3.753418388256828 \n"
     ]
    }
   ],
   "source": [
    "def integrand_LN(S, strike, e_ret, vol, payoff):\n",
    "    if payoff == \"call\":\n",
    "        return (S - strike) * ss.lognorm.pdf(S, vol, scale=np.exp(e_ret))\n",
    "    elif payoff == \"put\":\n",
    "        return (strike - S) * ss.lognorm.pdf(S, vol, scale=np.exp(e_ret))\n",
    "\n",
    "\n",
    "call = quad(integrand_LN, K, np.inf, args=(K, e_ret, vol, \"call\"))[0] * np.exp(-r * T)\n",
    "put = quad(integrand_LN, 0, K, args=(K, e_ret, vol, \"put\"))[0] * np.exp(-r * T)\n",
    "\n",
    "print(\"Call price: {} \\nPut price: {} \".format(call, put))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The put option payoff $(K-S_T)^+$ is positive for $S_T < K$.    \n",
    "- In the call case, the integration is from $K$ to $\\infty$.\n",
    "- In the put case, the integration is from $0$ to $K$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we use the change of measure proposed above?  In this way the integrations are simpler.    \n",
    "Let us compute $\\tilde{\\mathbb{Q}}( S_T > K )$ and $\\mathbb{Q}( S_T > K )$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Risk neutral probability under stock numeraire,\n",
      " Q1 = 0.7257468822499276\n",
      "Risk neutral probability under money market numeraire,\n",
      " Q2 = 0.6554217416103069\n",
      "BS call price:  13.26967658466257\n"
     ]
    }
   ],
   "source": [
    "# expected return of the log-price under the new measure\n",
    "e_ret_1 = np.log(S0) + (r + 0.5 * sig**2) * T\n",
    "\n",
    "Q1 = quad(lambda S: ss.lognorm.pdf(S, vol, scale=np.exp(e_ret_1)), K, np.inf)[0]\n",
    "print(\"Risk neutral probability under stock numeraire,\\n Q1 =\", Q1)\n",
    "Q2 = quad(lambda S: ss.lognorm.pdf(S, vol, scale=np.exp(e_ret)), K, np.inf)[0]\n",
    "print(\"Risk neutral probability under money market numeraire,\\n Q2 =\", Q2)\n",
    "\n",
    "print(\"BS call price: \", S0 * Q1 - K * np.exp(-r * T) * Q2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is quite common to compute the Black-Scholes formula using $N(d_1)$ and $N(d_2)$.   \n",
    "The reason is that the cumulative function of the standard Normal distribution is more accessible (I guess). In the `BS_pricer` class I used the function `scipy.stats.norm.cdf`.     \n",
    "\n",
    "For completeness, let me recall that if $X_T$ is a Normal random variable, then $S_T = S_0 e^{X_T}$ is Log-Normal. Therefore we have:\n",
    "\n",
    "$$ \\mathbb{Q}( S_T > K ) = \\mathbb{Q}\\biggl( S_0 e^{X_T} > K \\biggr) = \\mathbb{Q}\\biggl( X_T > \\log \\frac{K}{S_0} \\biggr). $$\n",
    "\n",
    "This permits to use the Normal cumulative function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "## Monte Carlo method\n",
    "\n",
    "I'm going to simulate the random variables: \n",
    "\n",
    "$$ S_T^i = S_0 e^{(r -\\frac{1}{2}\\sigma^2)T + \\sigma W_{T}^i} $$\n",
    "\n",
    "for $1 \\leq i \\leq N$.    \n",
    "Then use the approximation for a call option:\n",
    "\n",
    "$$ \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_0 \\biggr] \\; \n",
    "\\approx \\; \\frac{1}{N} \\sum_{i=1}^N (S_T^i - K)^+\n",
    "$$\n",
    "\n",
    "For a put option I use this payoff $(K - S_T )^+$ inside the expectation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=44)  # seed for random number generation\n",
    "N = 10000000  # Number of random variables\n",
    "\n",
    "W = ss.norm.rvs((r - 0.5 * sig**2) * T, np.sqrt(T) * sig, N)\n",
    "S_T = S0 * np.exp(W)\n",
    "\n",
    "call = np.mean(np.exp(-r * T) * np.maximum(S_T - K, 0))\n",
    "put = np.mean(np.exp(-r * T) * np.maximum(K - S_T, 0))\n",
    "call_err = ss.sem(np.exp(-r * T) * np.maximum(S_T - K, 0))  # standard error\n",
    "put_err = ss.sem(np.exp(-r * T) * np.maximum(K - S_T, 0))  # standard error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call price: 13.263338006636662, with error: 0.005093638687208466\n",
      "Put price: 3.7553894006350093, with error: 0.002214066662789331\n"
     ]
    }
   ],
   "source": [
    "print(\"Call price: {}, with error: {}\".format(call, call_err))\n",
    "print(\"Put price: {}, with error: {}\".format(put, put_err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BS_pricer\n",
    "\n",
    "In the next notebooks I will present better the class `BS_pricer`. But now let's have a look at the prices obtained by different pricing methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creates the object with the parameters of the option\n",
    "opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\")\n",
    "# Creates the object with the parameters of the process\n",
    "diff_param = Diffusion_process(r=0.1, sig=0.2)\n",
    "# Creates the pricer object\n",
    "BS = BS_pricer(opt_param, diff_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.269676584660893"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BS.closed_formula()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.269676584660623"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BS.Fourier_inversion()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([13.26753511]), array([0.00294085]), 0.7083957195281982)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BS.MC(N=30000000, Err=True, Time=True)\n",
    "# output is: price, standard error and execution time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uv/9+yzAMZ+z3v/996+abb7ZWrFhhhUIhS1EUq7Oz0/qLv/iL00b+lM8/GAxaL7zwgvX617/e8vv9Vl1dnfXXf/3XVjqdrhgLWB/4wAfmfZ/Zv7dlWdbg4KD1nve8x2pubrYURbFaW1utt73tbdbY2JgzZrG/02wcPHjQ+vM//3Ort7fX8vv9VjQatTZu3Gg98MADFePOxfpcKPpo//791g033GCFw2GrtrbW+rM/+zPrxIkT816L/fv3W3/2Z39mxWIxy+PxWJ2dndYtt9xi5fN5Z8zExIT1oQ99yOrp6bEURbHq6uqsDRs2WJ/61Kfm/BYuzg6CZVnWhaUhFxcC3d3drFu3jkcffXSpp/KKwS233MIPf/hD0un0Uk/FhYvzBjck1YULFy5cOHBJwYULFy5cOHDNRy5cuHDhwoGrKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwcuKbhw4cKFCwfyUk/AhQsXr15YllXxByBJEoIgLPHMXr1wScGFCxfnBCWhPlvQl/+ZpolpmhWPy19vmiaBQAC/379UX+NVD5cUXLhwMQeLFfDzHRuGQX9/P93d3QiC4Oz6S+9Zejz7vyiKGIaBYRhYluVqC0sElxRcuHiFYzECfiEhP/v1szGfgDdNk5MnT7Js2bIXZQoyTRNd11EU5UV/ZxcvHi4puHDxMsOZhPtswf5SBHzp/+xzp0NpzNkSQsmUJAgChmEgy7KrLSwBXFJw4WIJca4F/L59+2hqaqKhocE5N1u4n42AfzEoF+5ni5LZyNUWlg4uKbhwcY4wnzCffX4hR+tsAV8uUMvt6wsJ+NI5XdcRRRFZXrpb27IsRHFx0e6maaJpGpqmUSgU0DQNn8/nagtLCJcUXLiYB2cbSZNKpRAEwYmamc88Uzq/WAH/Yue9VELUsix0XSeTyQAwMTHhCHxN01BVteKxpmnoug7YpiZFUdA0DYCOjg7i8Th+v5+ampol+T6vVrik4OIVj5cSSTP79QtF0gwMDBAMBunq6gKo2ClfSCF9rkihFEV0OoE+33mwv69lWfT19aEoCh6PB0VR8Pv9RCIRFEWpOK8oCqIoYpomQ0ND9PX10d7eTn9/P7W1tUSjUVdbuIBwScHFywoXOpIGFifgSzv9xZpNzifmm2O5gF9IyM8+VyKYkuAuF+Yej4dgMDjvc+l0mj179rBx48aznntDQwMnT55kZGTE+Y1c38KFhUsKLpYUL9XROjQ0hN/vp7a2tuJ953OmXihH6/lGuR1+tkDP5/OcOHGCkydPVpwv+S5mC/HSn9/vn1fAv5iQ0peirQiCQE9PD8ePH8fr9SJJkutbuMBwScHFOcP5DpUsPy4J90Qi4exmlxovNtpG1/U5u/SFzDXz2eHLzTAAPp+PaDRacb70dyEEq2maL0ljamlp4fjx4xQKBces5GoLFw4uKbiYF9UQSbMYzH7dUqF0DeYT8GcS9GCbqGbv0svt8PMJ+PkE79atW2lubqauru5CXwIHL1ZTKK0XURRZtmwZBw8eRBRFNxLpAsMlhVcBzpWjtRzbtm3joosuIhwOA+cnkuZsv9+5xtk4WnO5HOPj4xw/fnxBO7zX6yUUCs3raJUk6ZzMeSmjj0p4qZoCQHt7OwcOHCCVStHS0uJqCxcQLim8zHAhImkW42gt3fhLGQ9fPp8z4XR2+IXOn84O7/F4Kuzwg4ODhMNhuru7l7TKZzWQwrmYQ0lzGh0dZeXKla62cAHhksIS4mwjaQqFAtls1tmdn69ImsWgFHa4FLAsq0KAp9NphoeHTxtRYxgGML8dXlEUgsHgvCaaxdrhR0dH8Xg8S06SsPQO9ApNQZJAlEErLPr15WUydF1nYmKChoYGxzznagvnF0u/gl9BON+O1ng8zsDAABs2bFjySJpzRQqlePjFhEjOZ4cHyGazqKpaEUlzNnb4VxKqSlOQZARZsdeJIMAZ1svs9WRZFi0tLRw9etQp2+FqC+cfLiksgKWIpDmTgJdlGcuyzpn9+aVAFMV5v9+Z7PDznSsJkfkcrWeyw+/bt49gMEh3d/eFvwhlWCqtaTaqYR6WZdHRs+wUIVgWyJ6z0hbA1jiam5sZHR1lcnKS+vp6ZxNRDRrZKxWv+iv7b//2b1x//fU0NjYuGEnT399PU1OTU5OlhHMdSXMmlAqFXSiU2+HnC5ns7+9nYGCg4vzZ2OFfajw8LL2ppNpQDZpCTX0DwXAEyyoWxhNFLNMAQQRr8evXNE0URaG7u5ujR49SX18P2Mlsbne284dXPSl8/vOfp62tjUgksqCAHxsbIxaLLbnaWorZfjEot8Mv1tFassPLsjyvnd3n81FTUzNHwF/o61QNu+NqwZKTguwh6PWTz+XwFjdRDiHIMmjqot/KNE0EQaCzs5O+vj6mpqaIxWKutnCesaRX9c477+Rzn/tcxbmmpiZGR0cBe4F/7nOf4xvf+AbxeJyrrrqKr371q6xdu9YZXygUuOOOO/je975HLpfjuuuu42tf+xrt7e2LmkMwGHTs0QtBkiRngS4lSqRQcridTSz87Hj42fb2s7XDb9++nYaGhooSza92LPX6KGHJ5qF4EESJQiGP4rE3DpZhIEhSkbiF02oLJUIrmSbLI9y6u7s5duwYsVgMcLWF84klp9q1a9fyxBNPOI/L7eX33HMPX/7yl3nggQdYuXIld911FzfccAOHDh1yInBuu+02HnnkER5++GFisRi33347N910Ezt27FiU7d3n85HL5U475qXs0M+E0uI/nTAvPVcqLfyb3/xm0Xb42UL+XPkjljL6aPY8XJzCkmkKitcxEymKxxbsZhkhWJb9vCSBfuZ7qTyRDaCrq4u+vj6mp6epq6tztYXziCW/orIs09zcPOe8ZVl85Stf4VOf+hRvfetbAXjwwQdpamrioYce4tZbbyWRSPDNb36T73znO1x//fUAfPe736Wjo4MnnniCG2+88YyfHwgEyGazpx1zNqRwOjv8QucXssOXZ7UqioJpmhw+fJirr77aEfBLJRSrhRSgOsxH1TAHWIp5CEUN4ZTfQACy6TSBUKiSEEwDRAkE44y+hdI9USKF2dpCSVt2tYVzjyUnhSNHjtDa2orX6+Wqq67i7rvvZtmyZfT19TE6Osob3/hGZ6zX6+Xaa69ly5Yt3HrrrezYsQNN0yrGtLa2sm7dOrZs2bJoUsjn8/M+V7LDA6RSKURRPGNEzens8B6PpyKS5mzt8LlcDsuynJr9S4lqIQVXIFTigmoKgmBrCOV+A6CQyxUJoczRbBhQLFlhiRIY85NCeXIkVObVlLSFeDxOTU2Nqy2cJyzp1bzqqqv49re/zcqVKxkbG+Ouu+5i8+bN7Nu3z/ErNDU1VbymqamJgYEB4FTC0OwKmeV+idmYnp7m8OHDTE5OMjk5ydjYGI8++ii/+MUv+OM//mO6u7sdQV8qPAZ2LHw8Hp9jh49Go/NG2pyPePjSey65M5HqIQWonl36UmN2Zvp5RTkhGJVmIl8ggJrPo3jLCKO0dk0DQZbtc6fRFuYjBUVR6Orq4tixY1xxxRWutnCesKSk8KY3vck5Xr9+PZs2baK3t5cHH3yQq6++Gpi7wBcjEE835uc//zl33HEH9fX11NfXk0gkiMVidHR00NjYSFtb2xw7/IEDB4hEInR2dr7Eb/zSUL6LWupchWohhWoSBks9lwtGCoJom4yKAn+236CQyyF7PPMQhokgSrYGsYBvYbamMPu7dHd38+STTzIzM0M0GmVgYICWlhYikcj5/c6vIlRVemcwGGT9+vUcOXLE8TPM3vGPj4872kNzczOqqhKPxxccMxs333wzw8PDvPDCC/zqV7/iuuuuY9OmTfzDP/wDr33ta50Kk+FwGJ/PhyRJiKLomIWWEqVd04XMVVgI1UIKLubivJKCaBMCFHf9Yimy6JTfQCn2QZhLGBKWaQICgiTb2sYCKEUezf4uHo+Hzs5Ojh07hiAI9Pf3k8lk3LV4DlFVpFAoFDhw4AAtLS309PTQ3NzM448/7jyvqipPPvkkmzdvBmDDhg0oilIxZmRkhL179zpjzgS/37+k0Udng3Lz0VLjQifSnQ7VcD2qaQ7nixQsQbQzk+HUrt/Z0Zc5mgWBXDZzijAcR7MJxdwfyzRAmhsGXl6kcSETbHd3N9PT0yQSCSdUvBo2ba8ULKn56I477uDNb34znZ2djI+Pc9ddd5FMJnn3u9+NIAjcdttt3H333axYsYIVK1Zw9913EwgEuPnmmwGIRqO8973v5fbbbycWi1FXV8cdd9zB+vXrnWikMyEYDJJIJE47ppSnsNSYrVovJapFU1hqk0014Xz+HoMZFb/HQ71C5a6/XMgXHc25bIZAcJajuYww5uQuUFkYEk5fftvr9dLe3s6xY8ecca5v4dxhSUnh5MmT/Pmf/zmTk5M0NDRw9dVX88wzzzjNzz/60Y+Sy+V4//vf7ySvPfbYY06OAsC9996LLMu87W1vc5LXHnjggUXb3AOBAGNjY6cdU1p0S41ShrVLCpWolnksNc6HpmBZFv1plcGMhk9Uifk9iEXT0LxC3rIIBENOQmg5Yczng0BWQJ+b5Xymngw9PT089dRTTi2wUr7PUvvaXglYUlJ4+OGHT/u8IAjceeed3HnnnQuO8fl83Hfffdx3330vag6LNR9Vi3q6UCG6C41qIYVq2hku9VzONSlYlsWRZIHRnI4iAIJAoqBR4+VUeOk8juZ8LovimRuqWuGDmGVSokxLgDOTgs/no729nRMnTjhEoOv6vH4IF2eHqvIpLAUCgcAZSaFazEdQPbb8aiEFF3NxLoSiaVkcTNiE4BXt98wbFkOJTGV46Rwhb6B4io5mw36+OPhU5FHRKY1lIkkiYlmJmdlNnE6HUmXcXC7n3BfVcG+83OGSwiJIoVoczVA9c6kmUqiWeSw1zpWmYJgW++J5JvI6fknAsEA1LSKKyJRqksoXZgn5sgQ1QUSSJAq57MKRR4IIFdFFwpxIpMWQgsdjO71PnDjhfGdd19318BLxqieFl6P5qBpIoZrMWNWAargW52IOmmmxJ54jrhoEJQHVtNAtiCgiSc1EBAYTORDEMiFfmaCWTibx+gMLRh5hGohSMbzaMBAlCVFWKkrOL6YAZemeHB8fJ5PJuNrCOcKrnhTOde2j841qEsbVMA+oDoFcDXipmkLBMNk9nSOpmYRkkaxhYZQRggx4JYHJgk46XzgVeTTLTBSKRNB1jfLchXJCkEplKSzTdloXiUMo8wcsRlMo3ZMtLS1O3gK42sJLxaueFPx+/4K1j0pwfQrzz6Mabrxq0RRg6efyUsqf5HSbELK6SVgRSesmFhAuEoJHAEkUyBkWIVmkL2lvpOZLUMvnsgiCOCd3QbBMpGL3QMu0zU+GYWAahp0JXawEDIsnBVEU6e3tZXR0lGw262oL5wCvelJYrKbgmo8qUS2kUC2ohmvxYkkhoxnsns6RN2y/QUozEYCQbB97RbAEgYJpOYQRzxvkCmqZo9lEEEV0XUOW7Qq+uWzGiTzKplOIkoSmaWTSaURJIpvJYOg6kiyTTiUJR2sYOHECODtSCAQCNDc3c/z4cVdbOAdwSeFl5miuFmHszqP68GJIIanahKCaFtEyv4FPhLRu4sFEMy0008JjqKQ0EywLUc1xcHyaQj5PPpdDECVSiQSCICIrComZGfyBoF1puJAnHIlg6DqiIBAKhzF0HX8ggMfrxTQMgqEwkiQRDIdJpVJnRQoAy5YtY3h42I1EOgd41decXYyjuZrMR9VCUNUkjKtlHtWA+QpIGoZRUd69dJwyBaZ9NSCIiPksCQJYuoZh6OS8fshnUT1eEEUkNYfq8YNl4rFMVI+fvGViWPbGyjR0QsWWtomZGaLF0taSAEoggGWaiJJtUio5lwVBcI4ty8LQNbp6lnF4/z48i6g0XE4KoVCIpqYmjh8/ztq1a50Kqm7ewtnjVU8KJfPR6XZZrvloLqqJFF5NME0TXdfnFfKZTAbDMNi5c2fF+fm69FmhGjJhu5Wq19Qp+ALIWIiKgiorhGSRjC+ARdHRjB8J8MoSWUPELwlopshQpsByr+I4mi3TIFpTg2kayKI4pxxGyX8wmxAwTSTZbiTl9QfIZ9JnRQpgawtbt26lt7cXr9fraAtulvPZwSWFQMDpllaKe56NahHE4EYfzTePasGLmctCu/j5OvSV9/iQJGlOh75SSGdTU9OcVqzlTZx2jqfQEBFMi6AsktYFfCIYiE4+QlKz13vJ0awUHc1Zw35NzjAxLcioOkaxEnYpd6FQyONVlDnNdUqEAFQSgmUiSBKmaSAg0NXTw87t2/D7fKe9drNJIRwO09DQwPHjx1mzZo1DoK62cHZ41ZNCqYtZNptdkBRKtVWqpblNNRBUtZACVIf5qLQ+TifY5zuerxVrSZjP7tRXLuTn2/0mEgni8Titra0LznHrSILfnJzh4voQzZEAad0kINlOZMM6RQgCECw6mj0igJ3RHJJFMsXIpKgiktBMhhIZOmtDjlYgCQKSLC+sFZSFos5JbBNFDF2noamJ5KyS+LNhGMYcbaK3t5dnnnmGZcuWudrCi4RLCkVSyOVy1NTUzDumtPCqofVftWgt1UIK55OkSxpkSYDPt3MvHWezWWZmZjh48CCiKM4r5AOBQIVgLz8+F9/jdJsWy7L41WCcZ0eT+CWBoXSeWMhXsesvCXkR8Ml2lJFPEtBNC92yI49SRQ0iUhwrCzCZ12i3QDTtshWy7EPXVKRiQtocraC85HZZBVWxOFaSJNo6Opk4Q6HK+YR9JBKhvr6e/v5+Vq9e7WoLLwKvelKQZRmPx3NaZ3M1NbdxzUdzsZh5nM7hutDxfP22ywV5eSvW48eP09TURFtb25KVcF6IFEzL4md9U+yeTBNSbOE7ldcpqBq6rDh+g5KQV0SBbIUGQYVJKSSXchcE5GLuwkQ6S2tNCEEQiE9NURuL2ZVLKwhhbsntcm3C0DRE2W6+k02laCw20VpIg18oQqm3t5dt27bR09ODx+Nxymov9Ybu5QL3KnHmCKRqIgXXfGSj3OGqqirj4+NnFPLzOVxLQt7n8xGJROYV/ovpt33ixAk8Hk/VCR7dtPjPYxMcjmeJemR0yySpGrSHvDw/luSqthiBsgQ1QTiVoDbbTCQCflmwNQhRAAEKpj32eCJPSzSIZZoOIWCWzEQmWHP7KlSYl3QdSVEcbSIUieD1+znZ38eyZcvm/W4LkUI0GqWuro7+/n5WrVrFc889R2dnJ93d3a62sAhU1wpeIpwpgU0QhKqJQHqlmo9erMO19Nvoul4hyMPh8LwCvtzheq6x1AJndreygmHyH0fG6U/miflkMppJ3jDpCHkZTBeQBRAwSWkUHc12raN5zUSAIglkdIuALKCbYJgQlkVSxV7LE+ksTZEQmqYhFv0KtlZgE8JsH0OFv6GY6Yxlgiih6xqmYSB7fei6Pi/Zni6Xobe3l+3bt9PT0+PUUXJ9C4uDSwrYpHCmUhfVIoyrZR6n01hKMeIvxeE62/a+kMP15MmTpFIp1q1bdyG//rzfealRPoesZvD9w2OMZFQaAwrxvI5mWg4heEWBsFdm51iCq1rr5jiaobLEhVBW4qJgWJjMMikpIkfiOeqDftRCgWAotKhQ1NnHkiyDZWEYJl6fj7pYHcPDw3R2ds75vqcjhZqaGmpqahgYGHBIwfUtLA4uKWA37DhTqYtqSWBbCvPRfA7XeDxONpvl0KFD8wp5oMLhWi7Ig8HgvOdfjMPVvcFPoWQeS6o63zs4xlReoyXoYSyrYlrQXiQEvyzik0QmcxrNAQ+aYWIgOGYiAQiUlbgwEVCLJTCyunUqd8EZK5Aukkc8W6A+HHIig86Um1DubyhpFoIg4PV6UQsFfP4ASHaNpNm7/DNlPS9fvpwdO3Y4GqIbibQ4uKTA4ktdvBLMR+fC4erxeOxCZsUbrNzhOjts8kII7WrYpVcDLMsiJ8h8Z/8IiaLfYChtF5hrDXo4mS4Q9tgCMV7QaQt6Gc+pHJ5Kc0lzlIRmIgEeSSCjm8UENTvyKKqIpHX7Opc0iFNjraL5CQ5PZxHVHLV1dafVCrAsu5BeWRSSoeuIkgSCQDqVIhiyHdeRSISR0VHa29oqvu+ZSKG2tpZIJEIymXTCysvJysX8qDpS+OIXv8gnP/lJPvzhD/OVr3wFsBf75z73Ob7xjW84vZq/+tWvsnbtWud1hUKBO+64g+9973tOr+avfe1rtLe3n/EzX071j2bP43QZrot1uJYLcr/f7zhcZ+/iy2/AsbExBgcHWb58+VJcBgfuzX0KUwWD56hFVQ06wl4GU7bfIOb3MJxRqfXKFAyTrG7SEfYynFYRAFGw/Q+lBLXcrAS1Go/k+BhKRfLKx5ZHKQUli2RBo+4MWsHsHgvlpS8wTYcQBMuitraOdHJuPaT58hRmo+RbKPlbShqHqy0sjKoihe3bt/ONb3yDiy++uOL8Pffcw5e//GUeeOABVq5cyV133cUNN9zAoUOHCIfDANx222088sgjPPzww8RiMW6//XZuuukmduzYccYFUE31j860i08mkxQKBZ555pl5M1xn2+LPl8N1qaOPqhFLSVAnUnkeGcmjITqE4BUFwh6ZsaxKvV8hpeoUDIuusJeTaRVJgPoiYUS8OZrCgTkJaiVCKJmU0nplMltQFsnpZoWPoaBBR7H66UJaQUWms3nKvFRq8SkAeqGA1+fDsixCkQjj4+M0Nzc739myrDPe23V1dYC9iamrq8M0TVdbOAOqhhTS6TTveMc7+Nd//Vfuuusu57xlWXzlK1/hU5/6FG9961sBePDBB2lqauKhhx7i1ltvJZFI8M1vfpPvfOc7XH/99QB897vfpaOjgyeeeIIbb7zxtJ99vspnn2uHq9frJRAIIAgCy5cvr9jFX+idTzWRQjXMYynnsGcixc/6p9EtqEFjMGULcI8kMpnXaA4oTOZ0dMuiK+zjZLqAR4SIV2Esq1LrkxlI5mkO+ysij6KKTQjlJqWKZLZieGq5jwFAzefJ6gYhSVpQK5gvCsnQNCRFAcsinUoSjdYUr6tFbW0tJ5LJilwMwzBQyvo7z4fS2KGhIVasWIFU9E+czyi0lzuqhhQ+8IEP8Ad/8Adcf/31FaTQ19fH6Ogob3zjG51zXq+Xa6+9li1btnDrrbeyY8cONE2rGNPa2sq6devYsmXLGUkhGAwuKvpI13Xy+fxpQyVP53CdvYsvOVxnm2lO53AdHh52dj1LiWohhVf7jf3k4DT/tKOfN/Y0IloGE6pCRJGwgJmCTmvQw2hWxbKgM+TlZLqAXxLwyRKTOY0Gv0KioKOaFpmCRkFREICIIpHWbTORKJwyE+VNC9OigjzCZSW3PSLkAyH64hnWNy1c/2iOv6EsT0ECotEaJ2pIEOyEzbpYHROTkzQ22IX8FuM0Lm2y/H4/g4ODToiqruvnLJP8lYaqIIWHH36Y559/nu3bt895bnR0FICmpqaK801NTQwMDDhjPB4PtbW1c8aUXj8blmWRTCaZnJwkkUjQ19fHfffdx7p16+jo6Jgj4AuFAtPT0xw5cqTC4Vou5P1+/7znz6WqWk3CuBrmAdWhKSwFfnp8gm/sHsQjCmiGQVK3CKCjWbZJp71IApIArSEvQxmVsCKCIBAv6DQHPEzkVIxiZNJzo0mu7azHU9QAPCJY2P6CoCySnUcrKPkYZECWbJOSpeZICX5ymo5PluaQADDX3yDLWJaJVKx/VMjnkWX5VP4CEAqFmZ6ccrSFs2nZuWzZMg4cOEBnZ6ej9bvawvxYclIYHBzkwx/+MI899hi+01RFnK9O/Jl+0IXG/O53v+O6665DVVVHcNfV1bFv3z78fj9tbW2Ow7Uk4E+cOEEwGGTZsmWLynA9X6gWh3e1kEI13dQXai6WZfH/PzTK9w6MEJBFYn4PvxqY4sbuOhKahF50JNuOZoEGv8JIRqXGK6MaJlnNoC1o+xIsoK1IHj5JQDUMdKTT1jxKzvYxFDOh84aFV7DISx50C04msqxoiM7RCqwKp7Pp+BsEQJBOlXGRikQBp8xOTS0txONxxz+wWFJoaGigr6+PwcFBurq6HNOuqy3MxZKTwo4dOxgfH2fDhg3OOcMweOqpp/i///f/cujQIcDWBlpaWpwx4+PjjvbQXKyREo/HK7SF8fFxNm/ePOczL7/8cvbv3099fT2RSIRPf/rTjI2Nce+99y44z9HRUURRXFJCAJcUXu0wLYv795zk0WMTRD0SfkVmMJWnt8ZPpqCji7KdoJYq4BMFIl6Z8ZxGvU8mpRkUDMvRIASgJehhKF0gKIvIosiO0Rle31lP7jRmonIfg53HAKpZclDbPZsjishIVqNT0/FI4mmikGxCEIuZ6SXfg9fnw9A1REkuOqDtdp9er5fRTPasSUGSJHp7e9m/fz8dHR2utnAaLHk7zuuuu449e/awa9cu5++KK67gHe94B7t27WLZsmU0Nzfz+OOPO69RVZUnn3zSEfgbNmxAUZSKMSMjI+zdu3deUggEAvT29hKN2rsYv9//skleq5aCeNUyj1cTORmmxX07Bnj02AQxv4IsioxmCqyqC9KfyPH8RMp2NBeFfMAjMZXXaQwozBRsQugI24QgCzgaRNRj5wYkVJ06r0JWNzCLRfBKkUfBslDUUhE8vySgW6CZEFJKTmcBcinHvDScyM6fm1DmgJaKmy1D1x1n9Ew8XkEI5U7q1vZ2EonEokihPNKosbERj8fDyZMngVOBIK+W9bNYLLmmEA6H55QoCAaDxGIx5/xtt93G3XffzYoVK1ixYgV33303gUCAm2++GbALYL33ve/l9ttvJxaLUVdXxx133MH69eudaKTT4eWUp+AWxJuLapjH+Z5DwTD50rY+to0maAl6yGgmSVXnoliQg1MZJAFiXom8bhAJ+BAQSBQM29GcUTEpZjQXQ1VDHonxnEbMK5PR7ZpIbSEPw2mVnJ5gU3vsVL/molYw28cwOxQVwI9Bzh92Mp0HMyptUQ1P0bdQLuCtYs6AIAhO4lqJBKI1NRUaAuCYnQRRJJlOn3UfZ0EQ6O3t5eDBg662cBosOSksBh/96EfJ5XK8//3vd5LXHnvsMSdHAeDee+9FlmXe9ra3OclrDzzwwKJCNRdb+6gUTbSUqCZyqgZh/GpAVjP4wjPH2DeZpiPsYyqnktVN1sZC7JtK45UEWoI++pM5FEw6/UFyulFhJiplNAdkEUWyS2c3+hXiBbsmUvnYgCKRNwzkYmnsrGFV+BhCsuDkMcyuf5TWAEPH51HI6BYeEUZSebpj4YoKqVYxcsje/Z8iBNM0EIutPY3ZuQ5F7dQyTVpaWhno6zvrlp1NTU0cPXqUoaEh2tvbXd/CPKhKUvjNb35T8VgQBO68807uvPPOBV/j8/m47777uO+++8768xZjPqoWYeyabebOo1pwPuaSKGh8bstRjs/kWBb1czKVRzUt1hQJIaRIRL0y/ckcrX6JE1mDVZJAvc+uc1SRoKZImECiYNAS8DBejDwqr5oa8ysMZ1S8UpaeuhD504Sizlf/SMTENA1yhoxPAt2EgVSe1rDXEbwVGoKhI0m2GNI1DbkYljoTj1NbV+fkKQhl616UJEzLor6hcVHmo/KNoSAILFu2jCNHjtDW1uZqC/NgyX0K1YDFmI+qxafgmo/molrmca4xkVX55FOHOT6TY2VtgIFkDs20WF0XZP9UmhqvTECRGEoXWF7jZzxvoFqQ0wwG0wU8okBtMUGtziejmhZpzaAtZOcuGJYdeVSqmlrjVRjLatR4ZcayBbBs53HOsCp8DGBrBSWns69Y/8gjggCgeIt1k0AvEsl4Vi2WsDglgM0iIViWhaHrDiFYlllGCDh5CvaxUCxZIdC7YoWT0b8Q5jMxtbS0IAgCw8PDwCnfggsbLimwuDIXr5SCeOcK1UIKr9Td3clUnk88dYihdIGL6oIciWcRgN6aAAenMzQGFAQBxrMqq+qCHE/k0C3o9An86sQU9T6bMCbzdoJaWjXIG2axSJ4KnIo8Csgi/uLYmE8hpxtkdZOpXGFOxrLtdLa1AkWweyzkiuYl0wIDEaGQI2/YtZCiHpGsYdGfzBc7oMllxfFkxxzk9F4ARFGyzbnFkPLZhFAao6kq2hnuyflIoeRbOH78eEVNpGq4r6oBLinw8nI0u+ajuaiGeZzLObwwnuTvnz3OZE5jbSzIgekMXkmgPezn6EyWtpCXrGYSz+usiQU5NJ1BBDoDEifyFvU+hYJuMFPQaQ56mM5rqMVeCrMjjyKKhCgIzBR0mgJ2dnMpbHX3eAqPYDfSmVcrKOYmBCS7OY9ugdfSsTw+u2ObR3Iqq4ZkkamcOidPwbLsY9M0K5LSLKvSZGSvN7Pi2Ov10tTcclp/4EJF81paWrAsi5GREef3c7UFGy4psLjaR9ViPiqRwlILwhIpLPU8XmnYOhTnf/7n8/z3kVHW1YfYN5UhpEjE/B76kzm6Iz6mchppzWBtLMT+qVOEcSJrUK8IGBY8PTRNe8jDWGaumShazF2o9clolm1Sag16mMhq6NYpp7MEZFSNlF7s3TxLKyjlJpTMS2FFpCDYPZZtQrDvl2AxQ7ovnrWFdDEs1d6ln7qvSkQhYGvvFSRgnkpiKx3LioKqqiSSqQWv50KlMERRdLQFgKmpKbZt21YV9/hSwyUF7AW4mOijajAflcwlS714S/NYalKoJvPRS53LL45P8BeP7CKjGaxvjJAq6NSW+Q1W1AQ4mS6QN0zWxIKOo7m+SBgtXpGsCUlVZ1k0QFq112u5mciniEzldRr8ChnVKJbDsB3RJtAW8jgF8+r8CttHEvglu/7RbK0gXMxoLpmXUpqdfyBredK6bWryCRYZ3UKwTCzTYDieRC0U0HQNURTJZNJOR7RMOm1fR1EkMTNDBQkIc4+np6YIhULU1tWhquq81/R0Yautra0YhsHo6KjTN8TVFlxSABZfJXWpBXFpHlA9wnip51Etc3ip+OHBEW79+R5M0+TixgjPjSboj2cQBIHxrMrquiDHZrKYpsWquiD7pzIVhLG8JkBcsyiYsCZmP79vIkljoNJMlCgYNAdOmZRsrUBFpEQeKn5JIKjITOQ0anwyWdVANS0CIk6PBZ+l272ZiySQ1EwwTQQ1h+X1Y+kaRj5H3hKwtAKWYWCIEoPJHBbg8did1fz+AB6PB00t4PP77baZmko4EpmXEJw6SqZBXSyGIAgUCgUSyeS813W+jm0liKLIsmXLOHbsmGNmcn0LLikANikUCoXTLoZqMR+5msL883g54992n+Ajv9yPVxJYEQuxezxJb02A44ksEY/EmliIg9N2glpPTYBDRUczRUfz6rogJ5I5NAu6/CL7pzIEZRFBAN20KiOPiu05DQtaA4rtYwCiisBIRsUvWFimQbygE0IjVdDYMRJHTyfIGFYxYzlNXrB7KUuGiq74ECwTnwSiPwi6hldREH1+fCIoHi/ICn5JwFQ8ZHS7p4FSLBZpGjqy4kGSJFLJJLLiKZpJzbI+C7OS2MRT3dwi0SjhaM28u/wzJbi1t7ej6zqJRMIhj1e7tuCSArb5CDits7lazEelBe6Swim8XOdgWRb/8OwxPve7I0S9Mq1hH/sn06ypDzKSKTBT0NF0g/1TafyySEvYx7FZjua1sRBH4lksCzp8AgM5k4gi4pMETqYKnJycIZHXyBsmNagMZWxnb1DPMZzVkCwDxdKJaxYBDAwgb4nEFCiIHkxBpN6vIPuDCIJgV1n1h+woJEXCkL3IooBfkdEECdHUEUQB1cIOS7XssNSgLJIv+h6Gklmn9IRh6E45C021NYRSnkIpFLVECLOP7VIYJXLQSabm+hbORAqiKNLT08Pk5KQz7tWuLbikgK0pwJlJoRoWilCqAeOSQsU8Xm4wLYtPP3WIf3yunwa/h4hH5mg8yyWNYY5MZ8lqBhuawvzk6DhtfpmwLHAimafFJzKRKZDWDLq8lq1BYBETdQbzFmHBwDQMpgoGrR44kFTxYtGowAweRKDBL5OR/QRlkZDXQ06Qqfcr6JKMagm0h7wkDMEpjTGS0zkczzhlsk9FIZl4RQFFtEtf+CQBSxCxRJmgLDhhqeUZ0GFZZFo1SeYLFXkKuq6heDxYlkUmnaamtnaexLVTx6Z5KpdBFCASiRAIBOZs3BbTsrOkLWia5qynV7O24JICdtMeQRBOSwpSWdjcUqMawlKrhRSqCQsRVCncMZfLkUwmGRmf4H/95Dm+vXeIJp+EYegMpvKsDkm8MJ7CMC16fbBjLEWdDJlMmvG8QZsXxgsmqgUrwgonVRG/JNAc9DJhytQrYIgSaVNgVW2QEdXepSuKzLiG4zyeyBvFIniQUA2aAwrxvI5qWHSGvYxkiyW1i6Ux5GKjnVIf5/KCeAh2FFJAElANC0sQkbQCGd1ySKAUlhqWRdsPAZxMZu0KqcXdvywrjjkoFA47Qrkyca2srLYkoap2S9HS/SCI4hxtYTGNeCRJIhqNkip77atZW6jKMhcXGqVKqWfSFGBxi+x8w9UUKnGh52BZ1pxe2pqmMT4+zvT0dEXnvdltVi1Z4Z9OGDyfMGj3SyR0i5RmcmnMz66pHF4RemuC7J/O0BXxk9F0tk2rvGVVjINTGRAo5iZkiXol/LLEUEalK+JjJJ1HNeGiWJADUxkkoLc2wK8GJrm+pwEQmMxp1HllssUieK1BDyPFvgqdYR9DmQIi0BjwMJRR8UkCAVliIqcRSWZoiwaLBfFs05Bh2SGn2SIJyFoBXfEClSQQKjsOygKTeYN0XiXolZ08BSwLSZadaxYMBudNXCtVS7X7OXud88FgEL14rcvv1zO17Cy9dmZmhsnJSerr653ubB6P59wsmpcRXFIo4kwRSNVECtWiKVRDAtu5MB/NFvJn+l8S8oIgOB32SppAKBTC7/cTjUYruvB5PB7Smsl7f76H5xMJLooFOZHMk9FMrmqt4dnhGcIeiZaQj/3TGVbWBhjNqCRVnatba8jpBpIg0FPj59B0lnq/gmXBaEalt8bPiWQezYSegMSBqQweUaAt7ONwPEudT0GwYFqdvwgeQEfYy1DG1gpqfQqjWZWgLCKJAtMFnTqvzFBapSMaJCSL5M1TmkBJ2IcVkRReuzyGIlWQQFq3K656i8lvEnAylWW1r8Yppe3kKQiCTQjlkUezyEGSRBQlUHneNPH5fKTSaaKRCGDv+L1e76LWQE1NDUePHqW+vr7o7zAWVYn1lQaXFIo4U6XUEhEs9Q4dqkNTKM1jqUkB5moKJXPNYgR86X9JGM0W5IqizOmlXfpfXkTtmWeeoauri1gsNu8cx9N53vLg75AiAS5pDHNgKo1qWFzZEuXZ4RliPoWwV+bwdIZ19SGOzWTJ6SabWmvZNjJDTjNZUR/i2EyOlqCHtGaQUg1W1QU5Es9gWtDlF+jLGgRlkTq/h75Ejuagh5xmsnUozhu66xnNqpjF9psn0wVEAVqCXoZnawUeCd20SKpGBZHM5FRC/pImIFRqAqU8BUMjLQgVJFBq15kzLJRip7bxnE5HQSXoUWxtodi/WVEU0ukUfn8AqRiF5OQsWHb/BUEQSKVShEKhitBVr89HNputyI5ezCbONE1qa2s5ceIEU1NTxGKxV6224JJCEWeqlFraGVdLBNKriRRKQn4+gZ5Kpcjn8+zcuXNeIT9bkHs8HoLBILW1tXP6aZ+vSpkD8Qx/9MBvOT6d4abGMFsm0oDF5U0Rto8kaAl5AIH+RI7LmiLsnUihmxZXtdSwbWSGWp9MRrObwXSGfUzkVHK66eQjSMCK2gBH4llCEgS9dje28jLbq+uCFIo5BiVCkEWBen9RK1BEJOGUVpDR7aY8zcVqqqXX7ZpI8YYuLz75VHG8ck0AQ0OXPRUk4BGAYvKbV8TJhrYjpHKsbvAW6yLZlVML+bxNCKWGPMV7jzJC0FSVQCDgCP7yAIxwJEIykSASDi96p1+qlNrd3c2xY8eIFXMgXo3agksKRSy2KF41CONqmceLJQXLshwzzHymGVVV59jrS4XLZgt4QbDbODY1Nc15riRkLhTm+6wDY0ne8uBvGUnl2dwV46lDo9Q119Ae8fP8WJKuiJ+0qjOVV7myJcpzIwkkQeDypijPjSZoCniQRZG+RI61DREm8yqaaTmEUDITHYlnicoAAmMZdVaZbXusZpqsb4w6/ZjDXtnRCgzTIqnZWsF0QUc3LdqCtl8BoL2Y6SwAWVVDsxS7HMUsTSCPB9E0EGWZvGHhE21nt27ajmnVtCOSApJNEmNZjc58Ab/X4+z4PcXAj0QiQaSYxEbx9y8JfrlYhns2IQiCgFzswVCKUlqMQC9pFO3t7fT19TE9Pe20/FxMBNMrCeeMFN785jeTy+V44okn5jy3detWNm/ezI4dO7j88svP1UeeU7ycymdXg08BKusfnUmwzxb+YH+P+Xby4XB4XnPNfEJ+enqaTCZDa2vrUlyC0+K5k9P8ybefJp5TuaarnqcHJol4ZdbUBXh6JMmquiDD6QIpVXf8Cj5JYGVdiF3jSToiPnKayVg6z+VNER7rG+d1nfU0Bb1Oglpt0UzUEvSSyBXImhYr6wIci2cxrFPZzYoIlmV3cAvKIh5ZZDpfqRW0FBPbyrUJKEUhqUhALKDw3GiCazvrEYsNeMo1AUFTsWQ7Wa6cBMqd0eXHIVlgKJ1nhc9b0TozlUwSjUbtC2mZFebbkoCemZlxWupWkINhUFtXRzKROG1GczlKn60oyrzagiRJrxpiOGek8N73vpe3vvWtDAwM0NXVVfHc/fffz6WXXlq1hAAvr/LZ59unULKlnkmwa5rGzp07nfBBSZLmmGQ8Hg8+n29e4b/UDvvziV8fG+Pmh7aSUQ02d8V4emCSWMBD1KdwbCTBuvowR+NZ8obJVS02IUQ8Eq0hP/sm0yyvDTBedDRvbImybSSBLEC9X+HgdIYar4xXEjmZytMZ8TGRVcmZ0BOUOTxtl9leXSyHEZBFYn4PxxM5mkJegh7F8RWc0gpsRzOU+Rs4FYVkt/CUGc9qBBWRgm4gSNIcTSBnyiCIcwT/fGGppeO0rtIWyhPw+QDIZjKEi47ixEycuro6oJIQ8rkcNTU1c86bxQqsYOcanI2mUBrX1dVFX18f8XicmpqaV522cM5I4aabbqKxsZEHHniAz372s875bDbL97//fe6+++5z9VHnBS+3+kdnMw/TNBcU7PP9X0jIl/6XImvS6TTLly+nrq7O2ckvBapBayqfw0/2DfGeH2xDN002dtSxZWCKtogPEDg+neHKjjpUw6RgmFzRHOXZkRlifoWIR+FIPMPa+hDHi47mEiH4JIHe2iBP9E2ysb0GzYCxrEpv1M+JVB7NtOjyQV9GRxagO2r3XSiFrQ6m8rSFvOydSHF1e2xBraC1LDehFIXkl0U8kshUXiPqkdFMk51jCV7TEaPgaAIiWd0EUcRjamR0Owy0vFNbuWO64rwiMpYp0O21I5cCxVBUUYC6YoJayXxYOvYVqxDMIYRSVrKuU9/QQE1t7aJ9CqX1qygKXV1dHDt2jCuuuMLRFl4t3dnOGSnIssy73vUuHnjgAT7zmc84F+8HP/gBqqryjne847Sv//rXv87Xv/51+vv7AVi7di2f+cxneNOb3gTYN93nPvc5vvGNbzh9mr/61a+ydu1a5z0KhQJ33HEH3/ve95w+zV/72tdob28/4/wX06e5WsxHgiA4TtYzhU7OFvLz7dgDgcCc84sR8n19fQQCAXzFHd5SoNpu0m/v6OND//U8iihwSUsN2wanWVYXJFXQmcjk2dQd45kT07xmeSOXFAvftYa8CAicSOa4tDHCvskUmmlHJm0bSRD2SDQHfeybTNNT4yckyxzL5FhVZzuXTQsuqrP7LngEaAn7ODpjh62axbDVnoiP4YxKwTCRsRiZ5SuQgPqAMicKKaxIWECioBPzyaQ129TUFFDI6wamIBY1gWKZ63wW1WdXCAjLlYLf6domzz1OayptER2PomCaJmoh7+QpJGZmTmU4l5FDOp0mHA5XkAYU/QOyLdpisRjiItbIbI2iu7ubJ5980jFRlbTnxeQ8vNxxTh3N73nPe/j7v/97fvOb3/CGN7wBsE1Hb33rW6mtrT3ta9vb2/nbv/1bli9fDsCDDz7IH/3RH7Fz507Wrl3LPffcw5e//GUeeOABVq5cyV133cUNN9zAoUOHCIfDANx222088sgjPPzww8RiMW6//XZuuukmduzYcUYBt9g+zefDfGSa5lnFyOu6TjweZ2Bg4KxCKM+1+lutIalLhW/sGOTup44S9kh01gbZOTzD6sYww8k8ybzGNd31PH1iiqAikcmqjOd1eqJ+0qrBdF7liuYoO0YTiAJOZFLMpxD0yByJZ1gdCzKYzHNoKsX6xigHis11VtYGODCdwS9A2CMxkMzTEvSS1nRSqsHymgD9yRy6abE2FuK3g9Nc0VpLzK9wMq2iCBD12a04y6OQar0yuWKSW2NAYTpvm5pKCW+6lWJjSw2pkmlIEUkRmJOnEJonUkkA/KWoJQH8osBkVqUlIqOrhVOJa5ZFTW2tbb4RBKfMRaFQcAiBWVpE6dg0DFrb2hgfGzvjbzfb9+DxeOjs7OTYsWNs2LDhVaUtnFNSWL16NZs3b+b+++/nDW94A8eOHeO3v/0tjz322Blf++Y3v7ni8Re+8AW+/vWv88wzz7BmzRq+8pWv8KlPfYq3vvWtgE0aTU1NPPTQQ9x6660kEgm++c1v8p3vfIfrr78egO9+97t0dHTwxBNPcOONN572889l9zXDMBa1gy/9LxGNLMtzBLnX6yUUClWcO3bsGLW1tXN8Nxca1UAK1XCDWpbFtw4lefjYMHUBD3V+D/vGklzSEuXQRJq8bjiEUONXaAx6eX54hjdf0snuqQxpzXDMRB5RYFUsxPNjSVqDXkzgRDLHxY1hDhZzG7ySyExBQxGhM+LncDxLrVfG1HXGC8YpH0MxFPXQdAYLWFustioLdle04YxdJtsnS0yW5yZoBvU+hYRq5ya0BO1mPaVaSCVTk18Syet2DsGpPAUTDyZpXagU/FQmrnkk2+cgCeAV7WS4wWSOlogffyBwKkRVFLFMk1w2S6iMBHw+H0axD4NTG6mMEErZ0aXyF2fCfPkM3d3dPPXUU04U1KtFWzjnIanvfe97+eAHP8hXv/pVvvWtb9HV1cV11113Vu9hGAY/+MEPyGQybNq0ib6+PkZHR3njG9/ojPF6vVx77bVs2bKFW2+9lR07dqBpWsWY1tZW1q1bx5YtW85ICsFgkORparKrqoppmiSTSTtO+jRCvyTky52tpf8lIT+fuWaxO3ml2OB8qVENpABLqykYpsnffG8rL4znaAp68MgyR6fSXNley87hGQzL4uquGE+fmKIp5MUnSxyeTHNZSw1HRhOkERxCCCkSbWEfeyZS9ET9JAo603mNDU1Rdo0nMCwck9KNPQotQR/HZnI0BTwUDJOEAR0BmZF0oSJsVRRgdW2Qg9MZ/JJAfcDLjpEZ1jRFwYL4LNNQc8DDRK7Usc3j9HSeG5FUQBJgdUPE2f1bagHV668Q/LMT10ShdCwgF4vpyYAgwHROJaqItlZQFOoIAqFwGFVVURQFQRTRdR1d1/H5fA4JlJODU0l1ZoaGhgYy6TTe0yShzedI9nq9tLe3c+zYMS6//PJXjbZwzknhbW97Gx/+8Id56KGHePDBB/nLv/zLRV/APXv2sGnTJvL5PKFQiB//+MesWbOGLVu2ANDU1FQxvqmpiYGBAQBGR0fxeDxzzFRNTU2Mjo7O+axCocDu3buZmJhgYmKC559/Hk3TePvb387rXvc6rrzySkfQl7SDUtG8bDZbIeTnC6GUZfm8RStUizCuhnks5c2p6gZ/ef9T/Pj5fi5qDmJ6/QwmsmzqjPHM4BSyIHB5Wy3PDE7TWRNANUwGZrJsbK9jx1Ac07L4w8u6+e3wDHU+hahX5tB0htV1QU6m8kUNwk5gkwS4rGhSqvMpHJ/J0RKB9rCXeF4noxm0e2Aoq2NSFooqCHTX2NpE2CMRVGync1PAg08Umchr85qGLEr+BpsQ2oJzI5KUYhiqZti7f0USyHv9iJjIojQncc0jggUUTAuvaP9uqmkntOkmqCacSGRZWxfA6/dXJK6VksicMOhiSQunzEV5P+cycqitrXXMs6cjhYUyn3t6enjqqaec7OlSOPVS+tHON845KYRCIf7n//yffPKTnySRSHDLLbcs+rWrVq1i165dzMzM8B//8R+8+93v5sknn3Seny0ASlmrp8NCY8bGxnjzm99MY2MjDQ0NTE1NEQgE6Orqoru7m66urjk7+QMHDuD3++np6Vn0dzofqJYoqGoghaVCpqDxjn/5Fb/aP8yq5ignplPUtgecfISgItFTH2LH8AwrYyEmsyrTOZVNnTG2nphCEQUuba1lMmWXohAFgb5EjosbwhyazlAwTK5qsSOTSpFHO8eSTvbzkXiGK1qiDKTyFIxTWgGcCkX1SyJNQS/HZ3LEfHZTntGMSkfYx2ROZSCRobcuVGYaKiOBOWGpBRQBakoRScXubJM5jYlMnoaQn7xhgVpA8HjsUtpl4ao+SUArRir5JbuPdOm4YFiY2Md53WQ8maG5mMNSSmgTRRGfz0c+n8fr9aJ4PBQKhVNj5iucJ4qOEK+tqyOXzaLIc0VeqfrxfJs4n8/naAuXXnopx48fxzRNLr300lestnBetrLvfe97icfjXH/99XR2di76dR6Ph+XLl3PFFVfwxS9+kUsuuYR//Md/pLm5GWDOjn98fNzRHpqbm1FVlXg8vuCYcnR2djI2NsaePXv41a9+xfve9z7q6+v5u7/7O37/93+fxsZGamtrCQaDzsKrluijakteW2pc6DlMZwr84Vd+wa/2D3Nxex2D0xkyqsnqiI+nByap8Su01QbYO5ZkXVOE4VSe6ZzKNV02IQQUkdWNEXYMxZmIZ/HLEsPpApc32ZFHBcO0ayIVI486IgH2Tabpjvgo6BYj6QKXNYV5ZmimghBELLqCdh5DxCNR51cYTOVpCXrQTIupnMayqJ/RTIGcbqIbFlnNKPMVqAic6uksCxArlsHwSXaewkROI6SIeCWJeEEn4pEYSOTsMFFJwJIkDISKBjulstql3gqaeaq6ar5ICD4Rp//CyWTWSVQ0y7QFXdMc000ul3OOrTJNfjY5FAoFFEXBMAzyhcK8v2fpnl4oGGXZsmWMj4+TTqcdbeWV3G/hvJDCpk2bsCyLX/ziFy/pfUo/ak9PD83NzTz++OPOc6qq8uSTT7J582YANmzYgKIoFWNGRkbYu3evM+Z0eDmVuaimgnhLPY8LvVsbmcny+1/6Kdv7JtjQXc/B0Rlyqs6aBj/bD4/RHvUR8Xs4PJnm8tYajkymSat6MYHNdjS3RwPsGU2wuiHMaDpPnSKxsSXK82NJBE6ZiWI+hVqfhyPxDKvqgkzlNabzGlc0R9k1lqIvkWVtkRB8kkC9AgMZjZhPwSdLjlYwU9BJqjora+0oJM20uChm+xjSqubkJkgCNPjtns4+SSBSRgKKJBIv6NR4ZEAgpRnEfDJ5wySjm2QKKqphIUgyPkxHwAdl239gYoeo5gycrOZSz4WgJJA37fNhRUKXfUync3NKWEiyjCzL5HM5vF7vnNpIs8nBsixCoVCFKUmfJ3qw5ANcyNzr8/loa2tzejlLkoRhGFWxITofqJoUvU9+8pP89re/pb+/nz179vCpT32K3/zmN7zjHe9AEARuu+027r77bn784x+zd+9ebrnlFgKBADfffDMA0WiU9773vdx+++388pe/ZOfOnbzzne9k/fr1TjTS6bDY6KNqyGiuJnKqhhvjQs3h+ESSG//hv9k/PMPVvY3sHJjCsiwu765n/0SOsEemMxLgxEyWqzrq2D2SQCtLYGsKeYl6FQ5PprmkJUp/PEuyoGEVNLYXE9RWxULsLEYeKZLIiWSO9Q1h+hM5UqrBVS12TaSSj+HIdIaQIlHn9zCuCTT4JEwLWyuoOaUVrI4FOVzMaVhdZ/dbkAWYyqpM53W8okCNV2E8Z4eleiSR6SIJmBakVIN6n0zBMMnpJo1+hUTBQDUsmgMKeybSiAKY2RR5BKesdknwRxSRrGH/TqHieefYKMt21gwQBLsJz6yaRoIgoBYKeLxeRFG079dyQphFDqIoOmHmkizbkX+qOud3NcvGL4Senh7GxsZQVRVZlp1IpFciqqYg3tjYGH/xF3/ByMgI0WiUiy++mJ///OfccMMNAHz0ox8ll8vx/ve/30lee+yxx5wcBYB7770XWZZ529ve5iSvPfDAA4vKtH05aQrVMo9qIIULpSnsPTnNH//TY4wlc1yzvImnj44R8Ej0NkbZ0T9Je0QhreqkE1k2d8XYMjCFVxJY02QnsJU7mkuRSbppsakzxhNHx7hufTtpzbIT1Moijy5virB7PIlhwcaiSckviSyrDbBzLElz0MM1HfX0J3M0yBZZ3SJv2FrB0ZliYlux6Y4ILK+1M519kkBT0Mvh6SxdUT8IdsZyeVhqZUSS7Yw2LGgJeBgtdmdrDXoYLibCGYaBGLDvx/Ls5ahyqvtaeaJb+XFQxBlPPkPKFySjagQUuSIpzVPsjbBg3aOy49KuvrROZVGkpqaGXC5XQQDlNZcWQiAQoKWlhampqYp+C6/ESKSqIYVvfvObp31eEATuvPNO7rzzzgXH+Hw+7rvvPu67776z/vyXU0G8ahDG1TSP841nj43xZ199gpmsyjUrmnj6yBg1AQ9NET97Tk6zrq2Wo2Mz5HWLNQIMFCN9Sgls5Y7mzUVHsyjAxvY6tp6YoiHoRdJNjsSzsyKP7PBTEdjQbB9HPBKNQS/7JtN0RvxkNZ2CbieonUhkMbCc7GY4pRUoIrSHT0UhhTwyA8k8DX6Fo9MZmiKByoxlv8JUXke37GqpY1ltDgmUV1FtC3nYPZ5ifWOYoCySKm6iI3MIYe5xyZQEtvkoRRCAkzNZVjXaRfEq6h7l8xV1j+YjhJJz2uv1YpnFktuyTKFQQFXViuihxfZc6O3tZWhoCMMwnM97JeYtVI35aKmx2NpHrvnoFKqFFM7nHJ7YOcBfP/g7ZrIqm3obefrIGE0RHzUBD4dGE1zeFePwWIK8brGxO8aWo+MsD3lpCvvZV3Q0D6VyjqN5y4kpvLLI+uYatp2cpj3qRxEFnjg4zFUtUY4nsqQ1g6taa9g2kkARBdY1hNkxmqDBbxfUOxrPsqI2wExeYzKnMZVTGcsUMBBYHvE4mc4rilpBQBZpDvroS+So8yl4JZGRdIHWoJecbtKXyNPoU0ioNiG0Bj2M5zR0y6Ij5GW0SAhtCxCC7ZhWyWoGqfg0WdNOXAsrp8xEAekUCcw+zjjkYJuPLMvCJ5iM5TTyWmVRO7MYigqQTqUqymmXk0PJlJRKJp0eDKZpIssy0Wi0Ys0stthdqRzM5ORkhTZSDffAuYRLCkX4/f4z1j6qFmFcLfOoBlI4n6r7j54+zP/825/QFFC4oqeBrcfG6agLIggC/ZNprlrWwK4T0xiGyep6H9v6p2iNBpiaStE3neHy1lqOTKbtSqmdtqM54pVZVhdi18gMy2MhcprBcCrPFe116Jpe0Y0tpIj01gZ4YSJFW8iLIMBgMs+6+hAnU3mSxZLb20ZmaPArtCkGR5MqHlGgK+q3eyx4JMLFpjtNAQ+6aTGZ0+iK+JjOa6Q1gxW1AQ5M2Y192kJ2FzYL6Cgeg60hDGWK0UnFPAURaArYjmm56KQ+kbOFil0gz0LEDjXNGgsfC9jRR5liAhyFHHnLFk1DyeypshVl5BCPxwkVTcel87PJQVdVwsXObKXzkiSRz+dRy3wLZ9NiV1EU4vE4uVyuQlt4JcElhSIWoylUi/nIDUmtxPmYw/2P7eH/d+/PkEUBK6exo3+C5U0RMgWd0USOzcubePb4BB5JYH1HjIOTebrqAmimyd4T01zfU8+ukTiaaXJVRx1bTkxRH/BQH/SyfzzJ2sYIY+k8U1mVzV0xtg1Os//kNBucBDWZhoCXg1MZemsCZDSD8azKZY0RDk5nyOkmV7fW8NyoXVI7UdAY0iQCkkBDwO6xUO9XkESRsYxKR9hLSrWjkJbXBBhKF8gbdhmMI/EsR6aztBdDUQXsENXhouBvDtgaghOdlFXxiHYV1bGshlcUiHhlxnMaWcNEwSRn2FnKimhHH8lC2XHZeQnwiJA3QQJ8sojgCyBgEZBFhtIqeU2vKGFRap1pWRZqoTCnSqrTrKdYnn22FqEoCpFIxFk3Z1sWu7a2luPHj79itQWXFIoo+RRO9+NWi/moGkJBS/NY6pvhXGsKlmXxpR9t57Z/+RVhv4eupihb9p7kDSubGZ3JMp0pcM2KJrYcHSPiU1jWGGHXiSk6IgrxrMZEKs/m5U2MT6aRiwlqzw5O0xbx4ZUljk9nuKy1hmPTaVIF3TYpDUzhk0UaAl5Uw6Qp6MEnS/QlclwUCzKSKTBT0LmyJcqu8SSGaXFVaw3bR22n88q6EL8cmKJR1IqCtEBLyEvBMJnO27kJYxm7LeequgDHZrLoZWGpYPseBpM5pGLP5tLuv5Sn4BUFokXB75MEAorMVF4jKIt4iw17QoqIiEXfTBbbym5RMC0ky8A0DQqmZbfrNDQKpoWlFdDUAgUTTK2AJEJON7F0DUUQyOomEjCSys6pb2SaJpl0Go/XO7fDmmkiFx3MMzMzc3wOkiSRyWScxLaz0RQMw6CtrY2hoSHy+bxzD7yStAWXFIrw+/1OIbuFUC1mm2qZRzWQwrmEZVl8+tu/43P/voX6iI/6iJ+Dg9Nc3ttINpUnXdDZtNz2K8RCPurDPvYPz3BJRx3jGd2uhFokjGMnp7i0uYbnh+L01gUp6CZDyRwbO+p4YSRBXjfZNI9JycprGKbFcLrAJY12I56sZnBVSw3bRxJIosDlzXZYasQj0RbxsX8qTVvIy0xeZbJYEC+e10ipBitrAwwkc6hFEjg0ncXilANaEk5FJO0dT9IUsPsslOcpBGQRr2QL/qAEIhYzBZ2AYKEbBknVwIdOXtXQRIWReJJ0OomOgFXIYZgWpiAhaCqCIIKkIFsGkuJB9HhRsNe0aoJHFLAsE9UCRbBLZ5xIFlCL2kKJHDLpNKFiD2a9WBgPgDIBX3JIl3bz5eTg8/mcyMWz0RRM0yQUCtHQ0OBoC6X3eKXcCy4pFBEI2DXgT2dCcs1HlagGUjhXc9ANkw9+7Qnu+8nztMVCeBSZ46MJNq5qYXffBC8cHGZzbyNbj47TVhvAp4gcn0hxZU8D+4ftzOKN3TGePjJGXdBLU8SPYlmsaQwzkSkwmbUjj7YNTgMWV7bXsnWWSWl1Q5gXhuMoosgVzVH2TNh9FTaWlbtYU2+36mzwe4h6bafzspoAac3gmSmV5REPI+kC+WKF1MPFtpzlYaklB7RXtH0FR+NZApIdETQeT+LBBENnuqDjMe36X0nNwGuoFHSDrAEBdFQLCpZARLLQBRldkPAZeSzFS0ZQ8EsCktcPkoxfEhAUD5Yo4ZcETFHCRMAngQkgKZiFHKZlISpelFk1k0bT+Yr6RuFi1dJ8Pn+qQKRlVbTtLDmk5/M5lGsLZ6spSJJEb28vJ0+erNAWqsGKcC7gkkIR/mInp9M5m13z0dx5LDUpnAsUNJ13f+mnfOdX++ltjlLQDIan0my+qJVth0ZQJJGVbXVgmCxrCKPqJkPxLJt6G3mufwLLslhVdDS3RP2EvApHxpKYmXwxQU13Io/8ssi65hq2n4zTFvHjKZqULmmpYSCRYyavsSLi5bnRBFh2X4VSKGpXjV3uwnE6p/JcFAsymi6QKOj0+iGZ19BMi96wXe5CADp8gp2shkVMNjgSz+LFxI/BYFolKFooWEwUTPqTeSRRII9ERAJkBV2UiflkTMWLLkg0+hVUUUFHoCmgkDEFdAsafTIF0YtmwXROQzftTOZAWTkLp7SFU/cIDMAngKB40C0w8hlMQCvWTLKw60Jpun3vlZpMmaZJoFhmm2LY6WxTUiKRWDBCyefzEQqFFt1/uST4JUkiEolQX19Pf3+/oy3ouv6KuB9cUihClmUURTmtplAtZptqmkc13AQvZQ6pnMqffuG/eOTZY1zUEWMimWMymeOaNW1sOTBMxK+wrKWGXcfHMbMqk+k8E6k816xoYuuxcXyyxNq2Og5N5umsC2BacGI6zcZlDWw/Os7KuuApM5FPpqs2yO6RGXrrQuR1g+Fkjivb69g3niSnGVzTFeOpo2OEFJE19XZfhZhPJuqROBrP0hGQSeRVxrMqywMiR6YzZHWDFX6Lozl4ZihOm2JwLKUhAS1egcG8hV+0+ztP6BJRj0TE72XGlGgKeJAVhYQh0B72MmMIeGWZBr9C1hJQTWgKeJgpnOqtMFkU+K1BD+NZDcOyNY6JvI4lCLQG7eS2ZEElNKtXs1Paolj+wgICEhQsEEQJK59F9PiKxfJENNNyyGEiU7Yr13XkYmlto1gTaXaTnWw2SzRq5zmUJ6iVTEmSJDnd2xajKZTWWWlsb28vg4ODFAqFV5S24JJCGc6UwOaajypRDZrCS3E0T81k+cA//JQn95zkkmWN9I0lSGZVNl/UytP7h4hF/NRHA+w/McUlPQ3sOjJKY8jnJLBF/Apd9WF2D9qO5kROYyyZY9PyJrYdn8CyoEmR7QS1gJc6v4eDEylWxYKMpXJMZVUuawrx3FAcw7RYV+fh6YEp8nmVdlFj72SamAKCaTCc1egOiEwUDNK6xbpaH8ezJroFGxpDHMkJiEB7NIDsD+KTBNoiPoYLFlGvTMTnYTSn0+hXQBCYyGm0FyOSEgW7A9x4xs41mMjkmc6XC/5ib4ViWW2TUzkL1qzjoJZ1wljH0wVyZaUtyhPXMmXH2WI9pJAsgNePIEpF7cLEsCAg2+RwJJ5FL2oL/kAA0zAQse/bkuZQ3oGtZBIuNw/NNiX5/X7q6+sJBoNnXC+zayRFo1Hq6upecdqCSwplOBMplIfELSVc81ElXswchsaT/I8PfZv/fGIvr1/Xzr6BSVRNZ+PKZrYcGKatLoRPkTg+muDKlc3sOzFFQdNZXhvg6SNjNIR9xII+Do7MsLY1ynhGJ5HT2NARZevRMTySQG/Mz+M7++kKSpi6Sn88y/KQRF/c7rZ2ab2fneO2s3ddfYC90yp1fpmmsJ+0KdNb4wdZIa7DJY1hhvIWecP2MeyN57GADc0Rdoyn8Usi7T7YM5XhZDJHrU/hRDFjWRRgLKvSHvKS1k0SBZ1lJRLQTVbUBjhR5ozeNZ4ioki0hcoEf6gye3m+42a/TEYJOOcH0wU03ZintMVcoghKkNbtMvd6OuloF0FZJKcXyUERiedVBEEgk04jiaJzT5bMOrO1hVQxwQ0W1hZSqRT19fVnXDMlUijXKnp7ezlx4gSqqr5itAWXFMpwpvpH5fHQS4lqMR9VAym8GE3h6MlpbvzfD3JoYJJN6zvQ8hqSCBf3NLDt8ChdjWHymsbQVJrLe+p47sgoWCarW8L8bkcfzUEFU9fom0yxss7ObC4YFuubAuwYTBDyiHTWBTk8laOrLkhbOMiUarGxvZa+jIlqwuauenZN5QkqEhc1RdkzmaUt7MOvKPTN5DB1E0kQmCnobChzOpc6rykCXNwYZsdo0olCOpG3TT2DyVyxJIWdsRwv9oIez9mawIqyiKRSnoJhwdr6EIfjdnRSTjOcjmutQc+cYyeJrazc9mjOjhBqKRs/kspVaAWVhFCseyRBpihHAyLIoQhgl7zI6KatRSgSqmFxNJ7BMAz8Pl/FfeD3+ykUChWEkMvlnAijM2kLjY2NZ1xL89VIqqmpoaamhoGBgVeMtuCSQhn8fv8Zo4+gOkihGhZdNZBCCfPNwzRNCoUCqVSK6elpRkdHeex3u7n+r7/JidEEl/bG2LpnkGNHh2mJeNh1fILOWg+TM1mmUgUu6YjwfN80PlmktznCgeEU9RE/HXUhpnIGVy1r4EhctSuP1vvYM5alIeyjsSbE0ckMa9tqmcyoDI4m7cijk3EsYGOn7XSu8Sm0Rf3sGU3QWxukYNhhqxtaazk8mSaAXQRvR5nTeftIgqAs0lsXZPd4qiIKqVEB1TAZyRSQBIupsozlE8kcqlFJAuV5Cmvqg45jemVtgKdOThP1iE7iWil7eTijInEqia283LYEBEzVOW4MKPQl8wiYBGfVOirXHEqEEPFIZIu3lqjm7IqpxfM5wyYHnySSyGtOj4Ryx3E5IZTMR7Mdz+WEUHq9LMuk0+kz7vArciHKsHz5cgYGBtA07RWhLVRNQbxqQCAQOG30UXlM8lKimsxHF3IelmXZ5Y/L+mGXSPzQoUNz+mWXEopkWcbj8XBgMMUn/20HmbzO5SsbeP7wBLVhH36Ph2AgwMWREIeHZsirBtdc1MrTB4apCXpprAlwaCjOms4Yg5NpIplThfG8ssia1lp2npiiNeoH0Q5VvawzxoGRGfKawcUddSTyql01tdmumtoc8uIp9mte0xjmZCJHsqBzdUcd205OY1qgqxq70wUUUeCimO10rvHKtm9iKkNbyItmWgym8qyqCzIwkyGv6VzaGOHX/VNc2lzL6rpTgr8Ulgqz8xTs/AVZgM6IXTTPK9rCbTSroggQ8drZyx5RIOyRGM/ZmczB4rFHFAhIAjN48YgQ9siMZzUUAUaSOZoiQQTsiKNMBTmUaiBBUrXvKz2dQA7ZDuKo1y7SBxCSJdK6wZF4BqGQJVZXVxFVVOrM5vF4nEjBQqFQQQ7zaQuZTAa/348kSWiatuBGp2Simo3a2loikQgDAwMsX77cSWYrVWh9ucElhTKcSVMQBKEqTDflu6GlXHQvVVMo7ahUVa0Q5uXHs8+BrbGVWqWWblJZlp2CZeW9shVFQRRFfr71CB/7xm8oaDpXr2vnmb0naa0PI0oCfcMzXN/bxG8Oj2KYJletauHpA8M01QTweWQOD8W5rLeRA4PT5DWDsCRwdCxJ2CvTEQuz88QULWGFvGEyncyzcVkDO/onMUzLKaJ39UWt9NZH2Dk8Q1dNgIJucmImy2UtNRyYSJLXTa4pNuIRgKs66niqb5L/sb6DjGHywkSKxoAHRRQ4PmPnJkzlVBIFnfX1YQ7HMxRMuKzRzmOwgM6wpyJjuZSn0FvMU/CIAh0RP0dnsvglgfqAl+OJHEFFJOpVeOrENK/rqkcUBKbyGn5ZxCMKTOV1ArKIIgpMlx3PqAaypeOXvUzldfySgFeWODKToz0SRCqre+QtIwe/CNky81G2SAiKUSCt2es7rEiO5qAIkMyr1C9QNrt0f6iq6hCCNSuHodzP4Pf7EUWRdDp92vDUhUgBbN/Czp076e7udnwbpdLaLze8/GZ8HvFyKZ9drgovNunmfGA+UigJ+cUIeFVVHZW/XIiXBHs4HJ4j4MuJAKBQKPD000+zbNmyBW/m7z++h7/+4iMIAly+qpVn9p6ku6WGTF5jYjLDpos72Pp8P+GGMMuaa3j20AidxXyEgfEkG1e1sOPoGKZlcfXqFp4+MMLrNvYwlFbZPxxnTWsNfRNJcrrO5uV2RrMkwJXFInqxkJf4TIYRRWZlfYjxdIGZvMbG9jp2DMUxLMshBI8osK45yrOD08T8HvI5lYPpAp0RH9minf+iWJD+RI6cblb0W1jht9g5ngbgiuYovzsZpznko6fmFAm0hn0ciWcJyiKxgIf+ZI6IR8KvSAym8tR6ZSRRYDhdIOZTkLCIFwwiioSBRUI1iCoSumUfRxQJo3gclEDVBRKqQUgRAdsnEpRFJrJ5agI+JEAu1j0qkUMpQimoiGQ02wwUkgXyop18Vk4IpWPVhK4yG3+JELxer6MtlKoUlBPFQtpCoVDA5/MhSVJFsbzZa3uhNVZXV0c4HGZgYIDe3l4SiQSZTIaenp6XnbbgkkIZFtt9rVpI4ULY803TnFeYl/phFwoFnnvuOee50k2oKEqFgFcUhUAgQDQanbObfylq9ple963/2MZt9z1GwKuwrL2OHQeHWdVVz+hUikS6wDWXdvL0C4MEfQqX9zTwyz0nWdFaw1Qyz3Q6z6aLWtl6cARFErh0WRPPHByhNRYiGc9yLJ7lsq4YB0bs0tlX99Sz5egYPllkdWst2/smaK0JIAoCh0YSvHHjMn43PENWs6umbjlhawVXd9Tx9MCU04Ph+eEZWsM+RFHgN0fH+INLOzk4nSWp2qahvZN2RdMrm6NsH00AOMcSsL4pwnPFukiv6ajj4HSWoCJS41XoT+So8cr4FYmhouC3gLGMSqNfoWBaxHMazUEPGc3g+bEEG5pryeomecOkziuT0e0S2+XHtV6JjGagCRI13lKHNoOoR8IEDkxneH3IhwkUTLtAniScIgePCBnNRMBCUHPkpSBYFrKpkyr+luXkkM/a5T/CvrkF70okUNp0eIv1kRbSFpLJJKFQCFEUyWQyC+7uT7cJEwSB3t5edu/eTVdXF8lkkrGxMTo7O1922sLLa7bnGS+XlpwlQfhiyKlkl19oFz/7uZJdvlzIl/6XEoY6OzsrCGApulHNJkjLsvi7f/kld3/tCTZcvZxUTmPP0TEuXtHE0cFpsnnNIYTasJ+G2gBjIwnWddfTN5ogk9e4Zk0bTx8YJuiVWdZSw46jY/Q0RUjnNXYdGeOG167iV4dHMUyLNQ1enumbJOJTaKsNsuvEFMsawqTydpG8K7rr6R+Kky0zEymiwMUtNTwzOE2dX6Eu4GXfWJKe2gBp1WAileeSliiFYo/lDc0Rnh+1TUPlDXgubYqwfTSBgsXyWIhdY0miXpl6v4e+mSw1XhlFsgvlNQY8mJbFeFalOeghrRqkNYP2sJfpnEZWN+mM+BjPqOQNk5hPQcAib9gtOKcLOrppVRw3+BXiBR3dhIClkdEENNOi3ieTNUwKhkWNVyaeUwl4PXhEOy+hRA4ixSqpgoAiWGh+2/+gCCaqZJfWC5URQkC0yIYiHI2nubgxuqC2UDqeHaY6W1sIh8PO60u9n+fTFk5nPgKIxWIEAgEGBwedcNeXo2+hqkjhi1/8Ij/60Y84ePAgfr+fzZs383d/93esWrXKGWNZFp/73Of4xje+4bTl/OpXv8ratWudMYVCgTvuuIPvfe97TlvOr33ta7S3t5/288/kU4DqMh+VFruu62c005T/B/t7zDbXKIpCMBicc65kl5+NwcFB4vE4jY2NF/T7l2O+m800TT5+z6P880NbaIqFiPo87Dg0yhUXtbL7yCi6aXH1+g6efmGQprogXo/M4RNTXL6qhamsSiavsblICCVH857+SVZ31DE8lXYS3JLJHFgWV/Y0sL1vgvqQl4jfw4GRGS5qrWFoOkMyr7Gpt5Fnjo9jWXDd1b38sm+SoCKxrC7EjqG4oxUcnUpzUUOYoaTtdC617fRMpPi99Z08OzKDwKkubB7R7un8/JgdlhpE58BUhoaAB68kcmwmi2aaXN5cw2CqQHvYS1I1yGhGheDvifgZSudRTYveGj8DyTy6abG8xk9fIo9PllhVH2asmLjWEvQ4x80Bu6+zaUFMgWlVxjItmgIKMwUD3bLJIaEavDCR4g1dMVQTDMvWDiwLVAtkATyyQMEQsQwdv8dDzgDLNPEKFulincpybcGyoGCYBCRp3hwEr9frFMsr98OVBHu5kC8UCs6GJpvNziv8z0QKgiCwfPly9uzZQ0dHh7NpWmoz79miqkjhySef5AMf+ABXXnkluq7zqU99ije+8Y3s37/fyTi85557+PKXv8wDDzzAypUrueuuu7jhhhs4dOiQE5N822238cgjj/Dwww8Ti8W4/fbbuemmm9ixY8dpf5wzRR/B+TcflRxUpxPwpV3Mtm3bnJjocrt8ubD3+/1zdviKopyTRVpNIaklaJrBBz77Qx5+dCcdrTVomsFzz/ex+bJuntl70q4yurqFZ/adpKs5SkE1ODGa4Kq17Ww/MMSmjb001QbZMsvRfElPA4eG4uRV3dYg9g9RF/Zx2apWtvdN0BCQkCU78ujSjhgHR+3Io1KUkiwKXNZdTyZdoNav0BD0smcsUaEVXNpSw8Gi03lTsW0n2G07VU1HEWBNsQtbSJFoDfvYM2GHpfpkkcGUQXvIS8G0OJnKs7w2wERWRTcteqJ+xrIqBcOsEPwragMcn7FDVFfVBThcrKK6qi7I4ekMFmBhkdMMJ5N5qKzxTnkTnpGMape5CNnlLyzsMNaJImk0+BSSBR1FlvFJoJWRgyAIFAwLEQvDNMgZJiIgYqIKtpgKFTuzAZjZNKlAiGPxDGvqwxXaQqkNZzabdSKRTqctxONxp5pqqd9CKRKpHIupplpfX4/P52NmZsbJqC4R08tFW6gqUvj5z39e8fhb3/oWjY2N7Nixg9e97nVYlsVXvvIVPvWpT/HWt74VgAcffJCmpiYeeughbr31VhKJBN/85jf5zne+w/XXXw/Ad7/7XTo6OnjiiSe48cYbF/z8QCDA+Pj4aef4YsxH8wn5hYR9qWpjyS4/ezcfDAapra1lZmaGFStWEI1GnUV8oRddNZGCZVnk8hq3/J+H+NmTB1jRXc9UPMt0Iss1G3rIF3T8HpllHXXsODjCys4YE/EM8VSezRd3sOWFQbyKhKjpbOufqnA0X7mymZ3HxtENk03FEhiRgIfGmgAy0NsQZiKZYSKbY2NPA88PTKKbFtcstwnBr0isbI6yvW+C7oYwDQ0RDk+mWd0QZrioFWxsr+P54bj9uqJ5SQSubLcb9KxtjrI8FmL3eIo6n0LYI3N4ujIstcVjkVQNkqrO2voQx2ay5HWTiUwBn8e286+sDXAkfqp8dnl00rzHsSAHpzJEfR7awj4nKa2iP3PZcQ0aY1l7HbYUiQJOaRTJiSSvaY85dY/8kl1MzyYHAcMwERSv7XMQBQrIWIaBVxJIF1sWeDEpBEIAaIbp1EYq1xZKZpv5aiLN1hZqa2sBKu67Um+V8s3TYnb8Jd/CCy+8QDAYdIjm5aQtVBUpzEYiYTvR6urqAOjr62N0dJQ3vvGNzhiv18u1117Lli1buPXWW9mxYweaplWMaW1tZd26dWzZsuWMpLAY81Ep/nmxETYlEplvx+73+x3BPttefzohf/ToUYLBoFPddSlQDaRQukbJdJ53/s2/87vn+li7opmBoWnSWZVrrujh6R39bLyih7bmKHuOjbO+t5Hjw3EyOY1rLu7k6RdOEA546GiK8tsd/bzutavYe2LadjSvbuGZQyOIgsDGlc1sPTBMQ9RP2O/h4OA019QEGE/lSRVMruqp59m+Cdt5vKyRp4/a9ZFaa4LsHpymOxYiV9Bp8coVWkHJ6Qw4xfO8ksDapijPnpym1q+g6QaaYdES9GIBA8kcvTUBJothqRfVBTkWT6NaRWf0RArdsp3RO0YTvGVlM0GPzIEzkUDZ8aq6AAeLeQ2pvMa0YouLCkIIncpebvQITOmeOWPKNYpar0JW00GUCMoCBdP2L3hF0C0LQxBBUxG8XgqGhSTYmoqKhIBdBymj25uAiMc2JfUnsqyoDVZoCyVCyOfzeL3eOdoCVAp5VVVRFMV5/e7du4lGoyxbtsxZa2cyH5XQ2NiIKIpks9mKJjwvF22haknBsiz+5m/+hte85jWsW7cOgNHRUQCampoqxjY1NTEwMOCM8Xg8DvuXjym9fjZM02R6eppUKkUqleKBBx6gra2N3t7eOcI+l8sxNTXF4cOHncqqs002wWBwXnv9uVwQ1ZDVXA2kADCTKvBH/+t+dh8c5vK1bew7MkZBM7j6sm6e3tFPU32YqYkkEyZsWN3CnmPjqJrBpvUdPP3CCWJRPzVhP/v7JljX24ipGkyn846ZyKdIrO6Ise3wKO31IUzT4vhogsuWNfLcwRGaljXSGRZ5tm8SjySwrj3GM8fHaQz7CHoVDo7MsKo5ylgyx0xW5SJVZ/t0pkIrkATY0FbH1hNTRDwy7TUBnh+eoSXsRRHtJLc31oeZMkziea0iLPUUCQgVzuirWmt4bsTeWKVVjRPpAmCbhkrZy6UGOyKwrBi6KgnQEw1waDrrHB+YztAS8tEcONWrubms5EVbyMtItrKfM8xPDlnd4KrWWnJFK6xPxCEHydQxRAnNtPsogIAqyVi6jleRyeim3WynkCMlFHugqDqGZTuqyyOR0um0c9/Npy2UyGFqaoq6skQ4TdNoa2tj7969dHV1VWgViymxLQgCwWCQmZkZZz4vJ22haknhgx/8IC+88AK/+93v5jw3W7guJolrvjG5XI6enh4mJycxDMPp3Xr06FHe8pa30N7ejqIoThiloigMDg4SCoVOGxd/IVANWc3VQAonh2f42ndeYPfhOBsv7WTHnpMIwBXrO3hm1wCdrTWomsGxgSn+x43reWxHPwJw5Zo2tu4ZtBPYRIFjJ6cdwvCMzHDNhh7bTORXaK8Ps+v4OMtbaoin80yl8mxc1cyOI2MYpsXahhA/OzRG0CPR0xDh+YFJ2muDGKZF32SKSzrqODyWIKcabFreyG/2DbF8dQsNYT9PD9g9FlY1hNl20s5NqPEr7B9P0l0TIKsZjKSyrG2M8PyJKaL1kTlhqc+NJrCAlT6LHaNJBGBji00IInBJU4TH+6d4y8pmPLLIoekMigDtET9H4lk7fyHk4+iMncncHPLOOfaIAqPpPFHT3r3HfMXSFgI0BjxFQrCIoDNsKxd2DaR5tIWQIlEwTBBEAsWENrC1gJwmgSjgkwR009YeFAF0wbLLawMyJprPJoSS4/lkMkt3TbBCC/D5fMiy7GgB8xGCYRjEYjHnuBRt19DQgNfrZWhoiM7OTud5j8ezqHVZ+ryhoSE6OjoAllRenA2qkhT+9//+3/zkJz/hqaeeqogYam5uBmxtoKWlxTk/Pj7uaA/Nzc1ODH25tjA+Ps7mzZsrPsfn8/GTn/yExsZGGhoa+OEPf8j999/Po48+uuDcxsfHnWiGpUS15EssJSkcPjrKH978VUbHE7z299bw2+f68XtlVixr5Lk9g6zsrmey6FfYfHk3gyem8Mgiq7oa2L5/iJ6WGtLFBLar1rWzff8QWBaXrWxBUw3qIz4iAS/7B6dZ2xnjxESKVM6OPNpyYBhJtE1K2/YOEQ15qI/42TsUZ0VThKl0gelMgSu7G9g1OIVmmI7TWRKgN+TjFyfsVpytET+7RhK0RWxT4LHpDKsbwoyk8iTyGpe31rBvLEnBMHldLMjvRhIVYakAG5rC7BhLIQkClzZG2DFqRyetjAXZOZYkIIuYlsWxmRwBWaTO76EvkSMoi9T4FPqTpzKZB5J5QopE2CMzkMw75/dPZ3hTTQBLEBjPaSiiQK3P7tssCRASIWEoCNh1j0r+hJZZDmm78qodTpopEYIk2P2ZBQG0AprgdfwMFmBJdhFCv0ehYEpgmQQ9suN4nsnbzmyRU76BEiGUNoSn8y2UxpUgCALLli3j0KFDtLe3O/fbYnf6pmnS2NjI8ePHaWtre9mYjqDKCuJZlsUHP/hBfvSjH/GrX/2Knp6eiud7enpobm7m8ccfd86pqsqTTz7pCPwNGzagKErFmJGREfbu3TuHFARBYOPGjXR3dzv2+TNFH1VDSCosvUCGpdUUnt99ghv/5B8ZHpnhouV1qAWdSNhHV3uMFw6OsG5lM8PjScfRvOX5fk6cnGZ9bxO7j4yyuque6VSOiXiGzRd38uzek8iiwKUrW3h230nIq3iLLTkvW9bIsZEZUjnVab7jUyTWd9tVVb2iQHtQ4thEmnVttYzMZJnOFOzObAMTaIbp9Hb2KxLr2uvYuu8k7VEfsYCXgxOpYh9ng6FkjktaogzMZEnkNa7uqGPXyAwFw+Sarnp2Dtq+hyuKYamyYOcp7BhLoQgWa2J2mYuQItIdDbB3Ik2NV6Yp6OW/j47REvQS9sicTOWp8coEiklstV4ZvywxXDz2ySIjmcrzUa/McDrPdLGERdgjMZXX8YoCUY9MwhAQsYj5ZMayGiKzyCFwihwE7HBSKJa2KDqeZUMD2YNhYTuPLbvJjlLMZyiYgGWCrpHRikX1itrCSDpbkaWcSCRQFAWv1+tEEs2nLRw5cmTe3uzNzc2IosjIyAiweJ9CaWzJJDU8PPyyIQSoMlL4wAc+wHe/+10eeughwuEwo6OjjI6OOgllgiBw2223cffdd/PjH/+YvXv3cssttxAIBLj55psBu/HFe9/7Xm6//XZ++ctfsnPnTt75zneyfv16JxppISzG0VwNyWvw6jYfPbXlMG9++31MTafZdOUy9h2aopDKE6sJcvD4OJevbedI/yTprMqmy7p5ekcf9bVBGmqCeASBi1c0MTCasDOaL+5kywsnCPkVVnbV8/yhEXrbaukbnELTTTauauaF/gnymsGm1a2OSWlZc5Rdx8fpaYqgGSZqVuPSjlqOjCVIF3SnM5tIsdzF0fFiU54Quwenifg8dIf99MUzrG2MMJ62+zhf2V7LvrFTXdieGbSL423uqufpE1OcmM6wqdU2GfkkO09h11iSsCLS5BHYP5WmzqcQ83s5HM/QFPAQUCT6Ejmag168kt1bodFvJ4VN5DSaAh5MCyaLx0bZcel8Q8DWAHaPp2jyK3hkiYRqEJBFPLLIdEFHwcInWEzm7fDZWp9dFE8EGotVVeEUOZxMZgnKglMZNayI6KIMgkBAFlENyyEHSxBAVjA1DdEyQfECdr+FUsG8yWLvB7B36qFQCEEQKiL6ZhNCLpdj//7982r+JW3h+PHjTqj4Yi0EpbpHvb29HD9+fMnv1bNBVZHC17/+dRKJBK9//etpaWlx/r7//e87Yz760Y9y22238f73v58rrriCoaEhHnvsMSdHAeDee+/lLW95C29729u45pprCAQCPPLII2dk+ZdLmYtqmcdSkMJ//+IF/uRdXyeTLbBxQw9btx+nvs7P+OgMuYLGVZd2svvgMIZhcuX6Drbu7KetOYrXI3N8cApR1znQN0GuoLFpne1orov4aakPs/fYOGu6G5iYyTIxneHyrhjbDtnBCVeuaGbrwWHqIz67G9vgNKvba5lOF5hI5JA1nZPxLAXdZHNRK/DJIuva69jeN0Fj2Edd0MvBkQQrmiJkVZ34VJrLW2s4Np0mpeps6ozx3Mn4LAe0wMaOulP9nZuiTCXzRDwS7RE/+ybTNPg91Pk8jKgCrUEviiQwkMzRGfGhWxbD6QLLon4ymsHTg3E6wl7SmslMQacj7CWp6iRUnY6QfZxU7fOp4vm2kJdscXxL0MtkrkBaM4h47PspVax1JAmQtUT8kkBAsbUIj4hjYppNDhnNQC3VPZIFUpoJgoCoFcjqJianWnLqpoUigiBYmKIMpolfFm3HM7ZvIakZjKfzDgGUMoplWXYS2crNR5qmOZnPCwn71tZWDMNgbGzsrMxHJa2ipaUFy7IcbePlgKoihRKLz/675ZZbnDGCIHDnnXcyMjJCPp/nySefdKKTSvD5fNx3331MTU2RzWZ55JFHHGfP6XCmJjtwKiR1qfFqNB/9+w+e5Z23fhMsuGRdB9t29NHb04CqmQyPJrlsRTPP7jqBRxZZu6KZ7XsG6e2MUSjoDI0l2HRZN7979jjL2+u44qJWtu4dpKU+RNCvcGRwmktXNnN8OE4yU+Caizs4cGQUv0diXXc924+M0hYLOSalS3oaGBhPkcgUuOaiVg6MZlleF+CqZQ1sOTpOxKfQ0xBh9+A0HXVBJFGkf7LSvBQSBeJZ1amQWkpWK9VC8kki61uibDsZJ1rq7zyaoG8iaTuG41naQ15kUeBkukCTAlndYCyjsrI2QDyvMZWzI5VGMyozBZ2YT0EUBLK6wbKon9GMSk437eOsfdxTPJ/VTXqiPiZyKhnNoCviYzqvsXVohia/Ql43yeomNR4Zw4K8JeDDRBTtonh+ScAv2+TgaA5FcmgqmpWmsgUCIk7FVEkrYJZpAaWWnD5JwLIEBNmDqakIlkGu1KSnLKltNJOHYvTR9PS0k79TCg0vJwTTNM+4+xdFke7ubo4fP+7kPiwGpfcVRZHe3l6OHTu25PfrYlFVpLDUeDlpCq8289G/fvPXvP/2fyfgV1i+rJGdL5xgzepWxidTJNMqm67s4fDBYSIhL93tMXYfHGbN8iYmptNMxjNcs6GHrTv78XkkOmpDPHdgmO6WGgzDYnAsycY1bew9Nk5e1YuhqoPEZzJc2tPI7uMT9LbUUNAMhqbSTnvOnKpzzRq774IigqwZPHt8wm7VGfJxYGSGFU0RMgWdkUSWDd0xDo/a5qXNK5p4tn+SFp/s5CZ4RIHLW+1aSBGvzLJYiF0jCZqCXmp9dn/nrmgAw7TwiwLLawJkdZPxrMrKGh8zBswUdNY1hBhI5kmpBpc0hjkaz5LVDS5tinBoOkP/TIaVtQH6kzk005pzPFA8tpvz5FENi+U1AYbSBQqGTSCpgoZq2v6DjG4L6CAmBgIZzSSsSIjCKXIoaQ6KAHVFn4MATGQLFEx7DYUVCaNICOVd1wKyiGpadiRSUWJZkoIIc7UF1WAqm0fXdWprayuylL1er5NIWlq3i9n9t7e3k8vlUFX1rEihVAivtbWVhoYGJ7Kp2uGSQhleTqRQDfO4EKRgWRb/7//7Y27/yHe5/OIOmhqj7Ds4zKUXd3C8f4JUusBFK+vYur2PmekMK7sbOHBsjEsvauX44DTJdIFrLrf9CpGQj662OrY/38ea7gZm0nnG4xk2re9g2/4hLMtyQlUbagLURwKg6azpjDExk2UymWPT6laeO2L3Xbh6dQtP7x8uJqh5+d0LJ9m0rAFFEumbTLG+vZbholZw9bJGdg5Moxom16xoZsuxcSQBhILOcyenCSkSKxvC7BieoSHgpT7oY3+RBARBoH8my6r6EImCxmi6QCqdYzxrJ65d3BCmL1mw+yk0RTgwmaZgmGxojvDCuN3G84rmKLvGkujFSJxEQbc7xtUFORzPzntc6tC2qjbAsZksummxqjbIYCrPs8MztATsQniaadHgU8gjoCFQ65VQTZOMPpccgorMZF5HFqC+2LEtU1CL5iN7ty/rBec4qNg9ms2itmBaICoeLE1FKUYslcaVXjOSzM0pklfSFnbs2FGxZhfjJ5Blme7ublRVPSufQmmsKIqsWbMGRVHObvEvEVxSKEMp+uh0wtY1H53C+SYF0zS5/fZ/5+///lFaWqJEg16OHh9n44Ye9h4YRtMNrry8mwOHp2ltjuL1KXhFgSsv7mDv4VEKqsbVl3bx9PP9NNQFidUEOHh8nM6mKD6PxEwqzzUXd7B1zyB+r8y63ia27x+ivTGCIkscH45j5AqcnEiRLEYebT04jCwKbFhul9GORfw01AQZmC7Q2xJFMS2GZ7Js6Krn0EiCTEHnmuVNdkE8YNPyJp4+dioK6enDo1zVVktLxM/esSTtUT+KLHI8nmFlfYikqjGaznNJc5QTiRwzeY0r22p5bjBOZ9jH5c12zoJmWqz0w84xu7fClS1RdhST2K5ssR3TFI93jCTQDWNRWc0X1QU5VCyLsSYW5OiMTRodYR85zRbWTQGFqYKGgUBENElpplNOu0QOIUVEFAVmVB2PYIegTuQ0RCz6JmbIFoW7qObR5ZK2UOyvABWOZ3R7p18olt32y6ITiRRWJOKqwXQ2z/T0dEVJbU3TmJiYIB6PV6yxxQj6zs5OTNM8YyBK6T1nl8h4OcElhTKUClidTluohh06vPLNR6qq8773/Rv/9m+/pru7HsOw+P/Y++/oSve0vhf8vO/OOeegnGNJVaqg093EhrYZBvAynuXhOmFPY2zGbZzw9Vxfg7nga2ZhvLDxAieMPQY8nuHOZUzoSPcpSVUqSaWcw5a0JW1taeec549X2keV6wDtrtNznrW0zk/aP+391tH7Pt/fk77flYUD7k90MLsQQi4TGer382QhhMepo1SucnqWRFGvM78algR1Bvw8WjzE7zahkMs4CMe5PRRgffccWaXGg6s0kVGnotVjYWknQqffQqFU4fQyw8SAj/n1U7o9Jh5ccR7pVHJ6Azbmds7xWfVolDL2zpK02tREUgWerp8w2enk6VFMigo6XUztnqOQCYy32pnZf7YLyWvWQqnCTixLl01PvlLnNFNk2G0inCqQKEggsB6VOpLuB63MnSSo1BvoBViIpKk3YMyhZ/vqtr3tNvHken7hai3wgcazCCRKFQ7T0i90X001wwfTztJa26TF6Lfp2YpLDvE6oliOpnBrpFRQvQGGeplMXaBab2AQaqRKVUq1Bup6hUJJaiGV1yo0ahXS1QayRh0NdWJ1GblsDr1CRl15U1jnuuX0KlpAihYQRUSlCmpVlDeihZuEeSepHCaT6RlAkMvlBAIBDg4OmvfZ2xaPryejT09P37j3+rm8+b4ft6R+RO0aFF43q/AuzSl8o6/j6wUK+XyJP/tn/wX/9b8+pqfHQzKZJxpN093pJpMpYjSoaW91sLhyTH+Ph1SmRCyeY/JuB3/w/jbD3R562p3Mr4bpbLFTKFY4jaa5f6uF+dUwtXodeb3B0m5EShOZtGyELhhod3AezxFLFXgwFGB27YRGQ5renb6i0fbZDayELulwmyhVa4Qvs4x1OjlJS5Tbw612qlfqYfc6JP4jnVJGr8/C3OHlM11I7Q4DlWqdh2snPAhYOcuWiBfK3PFZ2IimyVdqUkfSFQhIxeg4DWAyaOO/rZ/g1CgkaouLrKSt4JQEduQCDDslRlWFCIMOAwvnaZSiwIDDwJPTFA6NgnazpMksE6DDrGHrivKizaBiK55HANq0crauwMGnbDRBg0KOi2QaAH2tSEZU0kDAKFTJNkTqCJjlUJUpqIkyjAoRhUpFRVSgkYvoVApyyJABB7GU1FraaKCoV55RWss+Fy0gyhBqVeq1GsWraEErF8legYNRKSNTEzi7jDdrCNfW0tLC5eUl2aykUPdh2kwbjQapVIp0Ov3afde1g48jhW8CU6lUCILw2hDxXZlT+GYFhWQyz/d938/z+c+vMDwc4Pg4RjKZ58GDbqamtjFplThsBta3zhgdCrB/eEm+UOXe7VamHu9hMWuxG9WsbkcY6HJzfpkhlsxfFZoPUSpERnq9zDwNMdHjQaGQ0kRjPR52j+Nk8mVpdmFFYk0d6XbzhekdurxmjDol2ycJ+gM2LlIFLtMF7vV6WDy4pFJrcK/HzdTGKcV0nrEWO4/2olh0Snw2PSvhxDNdSH0eM5fZIhfZIuMtNmT1Btly9ZlIYPKKPrsBPAham8ypd/1Wpo6kdtVOo5r5SBqVKBBQw2JUml7utOpYjmbQyUXaTFpWLjLo5AJ+vZKViwxaGRxdJNhPFlDQwCLW2UsWkNHAIlQ5yJSQ0cCjhKNCDQEIaGSclKUTb4dRRaSuIFWX4dUpycqkE75N3iDdkNNAwKVRkK5BtQE2tZxirUGhWseokCEC6XINtSigV4okBBW1UhHKRSqilHu/qZ1wM1qgUvogWqjXUMpE8tU6AhIgXKeSDs4vXyjuqtVqvF5vM1p424G062fN4/Gwv7//xr2va3N91+2jedVfJxME4Y1tqe+CM76+jm+2mkL0IsXn/s6/59GjXcbH29jcPKNYrHD3bgfT09t4vRZiZwlCxzHujLWyunFCuVylt9PKo7kQbqcRg17N3Ow+YwN+9o4uyeRKTI5fF5pVdATtPF0/obPFTj5d5PQiw90BP0s7EUo3SPKMWiUdARtPtyMEnEY8Jg1H0Qyj7Q72I8lmjeHRdoRGo0GvW8OjrQh6tZxaReo2cl+xqW6fp+m+0YU0GrBxcJkhXahwr93B06M4m/vnvBf8IBJ4ELx2/DDhtzB9FEctExnxmHkcjqNTiHRZdTzcjWJUiLjUIodF0MvBLIfNWA69DHRCje1EHr0IOrHBfrqEUQ4mhYz5eAm/WsCsknNZE9HJBVw6FbGGHI1MwG/UcF4RUIrQYlRzXKg1I4q9tESuV603msNjJirEqhJoeHVKzq90FFwaBclSlXJdqjOUbtQZ5DKRVLmOXIDDyySoNNBooL9ROH4+WkCmoCGIyGlQr1Yp1uqIgjTZfA0IZqFC+eLlqZ7W1tZmS/vbpo+un/mWlhai0Si5XO6Vez/M5PO7aB+DwnP2pg6kdyV99K7UFP64ruHw+IJPf/8/4r99aZbJ97p4+jQENBgdbeHx4z3a2hxUKlU2N075jk/0MPf0EFEUGB0MsLkbJ+CTeK6OwnG625006nVK5apUaJ4PYbNocVj1rO+eNyOIx/MHfOtYi0RrwQckeTaTFodNz/rBBd1BG6lsidNwgoluNyuhS0k8Z8DH1OYpSrnIWIeTzUgBq06Fx6Jn9TBGr11HQxA4iucY8lk4uepCmmhzsHISl96j08Wj/QvqjQaddgOZQgmZAKNOPdNHcVQidJlVzIYT6OTgVgs8PUtikINJDuuXWSqVMh5Fg6N8DbMMtHIZp8U6To0cnVJBtCLg0SnRaZREyxIPkVal4qxYw61TUmiIXJRqV5QXck5zZYxKGRa1knCmhE4uYteqCKWLqGQCPoOavWQB+RU4bCfyZEsVPDolKaQTvu8G15FHqyRaqFBrgEMjJ1O+kue8mm3IVmpoRAGjUs55XUE5l0VJneyNwvHz0QKiiLxRA0GKFoRGHc1VtADQYlBhqL+6fVSv12O32wmFQm+dPrrODuj1etxu9zN1iZftff6zP64pfITt40jh7e2PK1LY2Arz6e/7R+yHzrl9q4NKpYpWq6S728PCQojeXi+xWJaLiwyTkz0kY1l0WgVdHS4Wlo/we/VkskUi0TQPJjqYnT9AUW80C80+lxGNSsHeUYxb/b4PIoixVkrF6jOdRz6HAY1awV44wXCHk3A0TTJbxGFUE0sXqAP3+qTZBL1aTrfPwvxeFKtWjlatYOcsSY/fwtFJgmimwGjAzGYkSa5UZdxvYvbgglq9wYhLx9TuOSLQY1Uys39B/iJOm17OYjSLXi7g0yvZTJSwquXYtCpCuRoevRKTVs1poU6LSYtKqSJfE/HrlNQFiBZrtJrUVBoC54UKbWYNhWqd81y5uY7kSrQY1ZRrDb5wcEmbUUMDifLCrlGglImc58uYVXI0Con3SK8QsagVHKWLqGUCHv0H4BDPl0kUK9BoYFfwDDPqWV6innBrlcQKVaoNabYhfzXbYGhGCzXkNDhPZSgLkkN9VbTQKBWoCSLVRgMZDahWKdYaEhW4SS3pUL+hq6itrY3j42MqlcpbneqvQeGa+uL09PSVtcePI4VvMnsT/9E1KHyjHfK7AE7Xp58/yv+LJwu7fPef+inOzhNM3utl6vEmKGt4PBZWV8OMjAQ5PLwknS5IdYXpbU4PLwn4rKxtnDLU7+MyViCZKjB5t4Pp2T10WiXVYpm1nQjtASvlSo1wJMXESJDlrTOK5Rr3x1qZWgiRiKZo9ZhZ2onQ7rNQrtYJR9Pc7vOycXhJvli5alsN49IqGW2z82jrDLNWid2gZvUwht+qodZoEI5l6XRoCUWS7IYTjNkVLIeTVGoNhl065sNS58+oz8jSeU4S0vGZ2IqXMWoUKGQqUnURl06F3aBhP13Gb9KgVsg5SpfosOioNiCcLj7TrporlBEFSFelzqCLfIVEsUKvTcd5Vppkvrnuseq4LFSIFyt0WrRUalKnkFevolJrkChWcWoUNJB4j6xqBSqZjEiujEEpw6xWcJz5ABy2E3mUAuipcHlV031eqjOSlzSdXVezDeV6A6tKihbyVYmyQquUE64pEWrVK06jF6MFnUIEpYoGAiqZgFyUXUULDXosGixqKVp5EyhYLBaMRiPJZPKtIoXrNJMgCOj1ehwOxyujhY9B4ZvM3sSUev3Hfhcc8rtwDfCHB4WvvL/C9/6f/hcSySz3J3qYerSJ22nmMpXi9DTBnTvtrK+fUCpVuHu3k+mZHTweE4IAWrWC8dEWtnYiFEs1JsZbmoVmn8fCwuIR7422cJmQeIwejLUyu3QkaSkMBZh5eojDoqNQKFMsVegJWogmclwk84x22pjfPKVSrTPYamJq+RiVQiB2fslS6BKbToFKDqGLLO0OHcl8hVShxkiLhcN4kVK1wf1eD6Kood6A+x1Ols9zKGUCo0EbiydpiVTPaWLlJIXLKHUkrZ8lGbJIJG6hRF5qUS3XOM0U6XcauMiXuMiVGbnRrnrLY2Y/nkMnNGjXCuwl8+QqNYadBvauJplvrocceg5S0p5Bh57jdJGvHcdoN2lIFqtkKzX8BhXZigQUbq2SSr1OrCiBg0IUXwAHlUzgLFMkd5U+cmtfpMoGKXV13b7qUCvIVaVUkl4hIiAVnsV6jctkqjml/Gy0IM0jCIKIkjqNhqS3IDbqlI620Ss+cMRvkxZqa2sjlUq9dfropqNvb28nHA439dJft/ejZh+DwnOm0WjeGCnANx4UPuqRwu9+aY4//ed/jlK5wu2xTmZmt2gJ2GkA+6EIn/hUF3NzBwgCjN5q5fHsHi0t0rzC0VEMq17N0+UjavU6vZ1WZucPrwrNKrb3zhns8xC7SJLOFhnvdzO9EEKlFGnzm3iycozDoqZerxIKJ7Ap6xxE0mQLFUY7rCzuxhAFGOlwsBpKYdarCLjMbB1n+ESvF1Eu5zxdZqTNwWmqRLZYpc+tYfkoIekm9HmZ2TxjY/ec++1OZvaiGFRyulwmFo5iOA1qbDqJBiNolXR8Q5dZul0mTs6TRLJFhlxGTjMF4oUyY14T+/Ec6VKVO35pZiFfqXE3YGU5kqJYrVPIlwkXJJrpcbeRlatJ5nHXs+u1yyzlWqM5+VysSWkoaRhM4j2KXvEeBQxqkuUqmbJUfyjX6sSfAwe9QoZFrWAtlkNeLmBRCETyL1Jle2/oNXu0SpKlKtV6A4tSRrnWIF+to5WLyKmzm6sjh5dEC9K6XshRF8QmJ1KfVUspm+by8rJ5f71NAdnhcCAIwmuLxtf2vKM3mUxYLJam4uPr9sLHNYWPtL2p0HxTsekbae9KTQE+PCj82n/9Ij/0uf8Vq1nPQG+QuYVduju9pDMFzqNJJu/2Eo0n0emUdHV7WVgI0dnpJJnMEY2mGR8L8rWvrGPQKelotbK5G8dl11IqlTgKJ+jptLKxHWF58ZhbvQ7m1yPodUr8HjM7R0na/GZqdYFYqsTEcICTszzVap3J4QCLe/FmjWFp7wK3TY9Rr2Y3nKC31U61WOEiVeBOl4u1oxjFcvWKEK+AANzt8TC1cYpWKafdbYJaHZtOhdOoZe002WxLPbjM0O0ykilWiKQKDPuthBM5tk4SfGebna3LLLmy5PiXziQt52sW1Uq9wYOgjcfHcWoNqXX10UkKr+LFSeb582fX9Qbc9piemXxevciwFc/SZZZ4j8r1Bu0mDWe5EsVqnaBR3YwingcHlUwCB51C5CJXJFFpvMCGejNa8OlURAsV6kiF53SlRrku6S0jCJSv2lHT2ewznEbX0YJRIUOu0dFAQCcX6bVq0SoVBINBQqFQ8x57m0nl61RQOp1+4z38ssijvb2dw8PDF9peP44UvsnsTaBw3X/8LpzS34VrgA8HCr/wb36Lv/4//UvUagWdnU6WVkP0dnk4PrkkkcwxMhhg6vEmBydhHE4da2th2trMHB/HSaUKjAx7mF84Qi4T6Ot0sL0Xw+81UCzXSaRK3LvdxvaeRGMwNtKCWqnBadXjsBrYO0ow0OXmMlEgnipw/1Yrs8vHnF9k+LaxVmm6Wa+ixWNmaeecVo+JRqPBUSTFSJeb0FmS2cVDPtHv48nOOdVanQe9HxDiDbfaebx1hlmnwu8wsBy6pJQpoFbI2Lt4ti1VAoE8iXyZO612Ns6S5MtV7rc7SaUK0jT0Tcff8sHMwmTQxvQVo+qDoI2pq7W8Wm5OMt+car65vuMxNXWbJ7wmFq5AQyuXka1IfEjdFi0HqQLVeoMOs5bTTIliTQKHxA1wuE4rXQvxbOelrijzFRuqgFRDuAYEv17VjCLcWgWXBUlb2ayU5DnzlRryehWNTGQzWUDkWQZUk1IiyRMEAa3YoMeiRXHlqIPBIIlEojlY9rZdRSqVikajwfn5+Wv3vSzysFgs6PV6jo6Onvn5Rx0U3kk5zm+kvQ199rsACu/CNVyDQq1Wa06Olsvl5tfN70ulEv/6N7/Mf/ndWUx6NVqNkkgsSk+ni72DKNVajZHBIEurRzjtRhRKOTaTEYvFxMrKMZVKjfv3Opl5tIvNpsds1lIu1Bjq97G9F6FUqjF5t4Opx3uoVXJ6utw8WQhx5047coVEcTE24GNt55xSuSqR5C2EUCpkDHa7SafyOM1atBolm6FLelrsnMeyJLNF7vT7eLp1RrUmRRPVchXZFf/R9OYpBrUCq1Zk8eASt1mLUiFj+yRBh8fE4VkSk8/KkN/C/kWGXKnKnVY7i8dxSZGtwynxIjVoUmLIZQKfGm/jqyHJ2V+zqArA3cAH8wvjPgvTV+shp56Hp1nudRsxq5XMRVLIBBi+mnAWkMjyrikvbl9FFCCBxlwkxbcG5fRYtU06i26Llp0r3qMOs4ZQqkit0SBgUHORL1Os1XFqlRSrdRKFChrqZEoV6lWQC2BWKZpsqF6dqpk+uhk52DVyEkUJHIxKOflilVwdxAaUSwXqSBKlxqvuI4BS/IJevwOZ+EFKRqlU4vP5CIVCDA8Pv/X8QaPRwGq1cnBwgMvlemWa51UpoY6ODlZWVmhpaWm+/lFPH30MCs/ZR0V97euZPmo0GlSr1Rcc+8u+B5iengYkfhiFQoFSqWx+aTQa9HoD//hf/D/5L787i9dlBQROz2PcH/OwuXQJAoyNdDC/uEdL0EGxWOHkNE5/Rwtf+r1tRFHg9u12Zh7t4vNaQIC9vSh3LDqOohlKNwrNRoMan8fM0mqYznYH+/tRFDYDd0eCzK2GqdXqzc4jvVZJi8/Kwpo0zKbVqwmdJRnpcrF9FKNQkmi0Z1aOAbg/5Gdq+Zj+ThdDLXZmtyPYDBrMOiV7kRRBh4FSpcbRRYaBoPVK07nCWL+Gr4YuKb8CBABJmGf3XHLYLXaq5RpyAW55LcwcSbTag24Tj46lIbZep4HZcAKNXKTbYWDxLIVKFHCpFTyOplHJBDotkj6zUpQU2hbO08hFgaErygsRGHEZm2R5mUqVekYaSut9jgNpO/4BOBymilQbDfwGFbFChUK1jl2jIF8s8fgsw3e2S7n6y6Kk3ezQKD+oM9wABLdWyflVy6pVLSdXqVMV5ahlAjJEtmI5hrwaaSjtKpXk0ihYP9xG1uJ+4b5tbW1lamqK7u7utwaFWq2Gw+Fgd3eXRCKB1Wp95b6XRR52ux2VSkU4HKalpaW59+NI4ZvItFrtG3Wa35VT+oe5hmtSsNc5+JvfXytU3XTy12uTydT8fmlpidu3b6PX61/60JQrFf7ez/5bfvO336ejxUMqk+MynubB7X6m59aZHBolnSoyv7hHd5eXaDRFMpVj8m4vX5lZxuFw4naZmJvbp73dSSZT4OIiw727ncw+2WPiU304bCpm5w9x2PQY9Go2tiMM9Hk5DMfJ5kp89/0ufm96B5lMYGI4wMxCCKtJi82sZW0nQlernVgiR6fPgsOsZXEnQuWqxjC1fIxMFBjr9TCzEsaoU1GvVIlnivisegQB9iIpAmYV6XyJZK7MWLuTteOYNCHd42Fh/YS6RvksCFzxIokC3G6VhHmUMoFBn5VH+xd0e8z0u0w8OUlgUMoImnUsnCYxquT4jBoWz1KY1HLceg1LZ6mrgTORP9iJEHCbMasVrF1m0StEvAaNRG0hF2mzaFm+yKAUBbqtEmjIgCGngbmzFN/b6cJnUN1gTNWy+ZLIod2k4ShTpFpv4NOrSJaq5BsiZqWMRr1BslpDIQiY1XIuClKfqlt7o9h8o/BsV8lIlmqSXkKtjChXk6s2EBoNxFqV3NUp269X4dLIWeflvEI6nQ673c7h4WFTQ+FtngulUkkwGGR/f/+1oPCyz7yeW9ja2iIQCDQPjB8VmuyX2TsJCl/72tf4uZ/7Oebn5zk7O+O3fuu3+L7v+77m641Gg5/8yZ/kV37lV0gkEty9e5d/+S//JQMDA809pVKJv/23/za//uu/TqFQ4Nu//dv5pV/6Jfx+/2s/W6vVkslkXrvnXZhqFgSBWq1GPp9/K0d/XQyTy+XPnOQVCgUajeYZR3/92nVf9puuQ6FQvBQQcoUi/+e/91NkU2X6OgOcRGKks3kmb/czNbeO2ahDpRVZmT5keKCF3YMI+XyJybvSvILRoKW/z8NXvrRJX5+Xk3CCdKbA5NW8gkolR6eU82gnhtdtAkFg//CSsZEga1tnUprobgc7W2eoVXJ6253MLh/jdRgQZSI7h5cMdrsJheNk82WMChlfWg3TaNAU2tGo5HQH7TxZP8Vh1qLXKtk8jPFtn+hm+STJZbrAcKudrXCMUrXB3W43c7vn1OoNJq+G3AA+PRLk85tnUtqn1cH0XhS1XKTPa2H24AKDSk7QbmDhKIZZq0RoNKhW69g0SswaBWvRNE6dCp1SzsZFBpdehVouY+syg0uvRiE2OMyWcelUtBnVPDnPYFUrMCjlbMdzmFRyHFolm7EcBoUMt17N6mUWtUyg3axjMZpBLkAsX24WiLtvAMLNyOEmOLQa1ZxmS1KxWKhSbYg8Ok1yx2dGIYrEi1VkgFWjeCZauAYEl0ZOtFClAVhUclKFGpWqNKEsNhpsX6bpdttoNaqxaxTN+/hV9YLW1lYWFhaw2WxNgsvX2XUE0NLSwle/+lUymcwz0r7X9rrIw+12s7Ozw9nZGT6fj1qthlqtfuNnv6v2ToJCLpdjZGSEv/gX/yJ/6k/9qRde/6f/9J/y8z//8/zqr/4q3d3d/PRP/zTf+Z3fydbWVvMP+rnPfY7f/u3f5jd+4zew2Wz8rb/1t/ie7/ke5ufnXxvaabVaotHoa6/v65U++sOc5h8/fvyCk3/+NH/ztT9ukq5XTTXHUxn+9I//TzxZ3eROfy/hSIxMNs/98T6m5tZx2c2o1Uq+Nr/MvTsDLCzuU6lWuXenm6nHmzjtJrRaFfFMipGRIFtbEg/SNSAYDGqCQTtf/sIKnUNe4qkS8USeu7fbmVs6lNJEt9uZeryHwaBmZKyNx0tHtPmtZPNlLi5SjA/4WL2uMYy38uWH2zjbHATdZmZWpKKz12ZgaSeC32mkXm9wcJqkv81BKHRJrFjhTpeLxf0LKrUG93s8zGxJWrzXgHBde7i4SKNRyOhxS1PNRrUCv0XH06MYNp0Ks1bF2kkCt1GDUi5jK5LiPbuBlELGXjxH0KylXK1zkMjRYtZSrNY4TOZpNWsp1OqEs2U8GhkNAQ4uM3h1Kmo0OEwXcGmVKOUiB6kCVrUCvVLGTiKHUSnDoVWxHsuikYu0mLRMnSb4/m43CpnI9hUg9Fi1L40cOi1aDpKSEE/AoCaSKVCp1LFrZGhkIvFSDaUIeoUULQiA80qGE54FB6dGQbxYpS7KmvMG2YpAvlTjU0pJkOf6GYFXg4LFYkGn05HP57FYLG+8f6+dvUqlwufzcXBwwPDw8Av7XpcSuo4W9vf3m5rOH9cU/pjtM5/5DJ/5zGde+lqj0eAXfuEX+Af/4B/wAz/wAwD8h//wH3C5XPzn//yf+exnP0sqleLf/tt/y3/8j/+R7/iO7wDgP/2n/0QgEOCLX/wi3/Vd3/XKz/7jTB81Gg1qtdpbO/mXneavnfr1af76+0KhwP7+Pg8ePPiG3nAvA4Wzixjf/zf+Aet7Ie4M9PJ0fZfh9j5kgsjM/AYBr8RjdBiOcm+sl0a+Tr1RZ3y0g0dPtvH7bNRrdUJHUSbGTezvxymVKty718nU9DY2mw6zWc/aWpiBAT+iUiCeyPPgbgfTT/aRy0Vu32phZm6/mVKSNxr0djg5PU+Tzha5NxpkdvmYer3Bg7FWpuZDqFVyhlsdfGEh9EHR+fCSLr+VWLpAPF3gVo+HjYMLiuUq3/nt/Xxx+ZhGAwY8Wma2zhAFuNMlsaWqFTJ6/VZmtyNY9Gr6ezzMX80p6FUK1s+S+MzSaXbvIk2rTU+hUuMonqXTaWD/NEFGq6bbruciVyJRqNDjMHCeKZIsVuh1GDjLlUgVK3SYVETzFTKFEgalHLtJOtm3mDTkKzVOsyW8OhXVRoOjdBGHRolSJrKXzGNWybGoFWxegUO+UuUyU0ME2s0fFJ57bgDCzYJ0s86AgEerIF2ps3KepstuQCYKxEtVZAJYrgrP8BwgXKWYGoCyWqIq01Cs1VHLRQbIkTo7xmfpB94MCoIg0NraysrKyls9FzdrBa2trTx8+JCuri40Gs0r973MvF4vu7u7nJ+ffyg67nfR3klQeJ0dHBwQiUT49Kc/3fyZSqXiU5/6FNPT03z2s59lfn6eSqXyzB6v18vg4CDT09OvBYU3Da9d0+Lm83lisdgLjv15p9+4kj981Wn++cLs257mr53xN/oE8jwo7IdP+b4f+x8JnUa4PzzAo6UNVAoFdruOz395ia5WH7Fkingy20wjjff10N8TZO7pHp1tHuLJDPGENOX86Mk294cHKRccPHq0i9drQRQF9vbOuXWrlY2NE5xeA3dvtzL9ZB+NWkF3h4u5p4f4vRbq9Qb7h5e43EYOTxIUipVm55EoCkyMBJleCGHUq/G6jIQOLgi4TFRrNUJnSQY7nIROk2QLZSb6fcxvnkqpoeEAqUQOGnC3283j7QgquUh/0M7j7QhGrRKvVc/iwQUukwaNWoFaEAhYdVRrDfYvM3Q4DKQKZS6zJXrdJs5SBVKFMoM+C6FYlmypyqc7XDw8TZKv1BjxmNi+zFK4Wm/FshSrdUbcJrYuMhRrdYZcRvbjOQJ2A91WLee5MtlKjXaThnixQrJUxW9QU6zWOMkWcWmVyESBg1QBs0qOWa3g9w8u+Z5OF0qZyG4y/wI4vCqVZBMqxIoC5XoDnVxEIxeJFauoREmj+bL4YrTg1siJFKTDkE0tJ16o06jVMShl/EC3G1nZzOzsLF1dXSgUimfkNV9lLpeLlZWVpmbC6+xmWkin0+FyuQiFQvT19b1y38tMFEVaW1vZ399HFMWPrMAOfARBIRKJANIf/qa5XK7mdGEkEkGpVL4QPrpcrubv37R0Ok00GiUajbK5uUk6nebv/b2/R09PDxMTE884+evTfDqdRq1WP+PUNRoNRqPxGSf/trn5D2vvwvAaPAsKq3t7/E+/+G8JnUSYvDXE1MIqRr0On9PO7Po6w32t7B9FyOaKTN4eYGpuDZNBR6Fa5CiUZqA3wFH4kky2IPEgPdpEq1GiMciZfrhFW5uDbLbExUWaiYl25udD1Gp1DGo5+4cxjAYNXreJpbUwnW0OEqk8sXiOO7daeDIfoms4iNWiY2o+hEopo7/TzezSEQ6rDr1WxeZelK4WGwaThvVQivFeDyt7UcpXKm3TV11ITcU2vYq7w0EebUfQKARaXWae7kdxmjTo1Eo2w3GCDgPlap3QeRqHRUuuVCOeKzHgNXMUz5EpVhgJWNk+T1Eo1xhvsbN6mqBUrXOn1c5RJEW+UmPCb2XhNEG13mAiYGXhLEm13uCOz8LTq3W/WcnmhTS9nM2VyMllZCuS7OZhukChWqfTrOU8XyJTrtFiVJMp1zjPl3HrlNJk9RU4KEQ4TBdRigJevYrdpCS402nRvlS2s9OkYS/VoHHVlRQvVAinC9i0KmSCQOIN0YJbpyKaK9EQRGwaBT/Q7UavlINGicFgIBwO09bW9lZDaaIoolQqicVibzw4PX+qb2trY3Z2lo6ODpRK5TP7bn7/MgsEAuzt7aFQKD7uPvpG2PN/6Lc5Nb9qj8fjoVKp4HK5kMvlyGQy9Ho97e3tGI3GF07z29vbGI3GZgvaN8LehQ4o+AAUHq+u8qf//t8n6PAyOSoBgt1iwqjXsbF/yFh/F9WsQDZX5P5YH1NzazhtZrRaFes7h3z63l2+9nCDYqnCg7sSIJiMOtxOE1+ZXmJ8vJednfMrYrwupqd3pDTR7Xbm5vaZ/PY+Ti5zbO5EGOj1cBSOk8mWuH+nnUdzB0CDFpeJ35vZxahT4feYebp+gt9tpl6vcxCOM9TtZv84zqjfxr1BP7PrJ9SvooLrLqTxXi/TK8foNQqCLhPUG9iNahTU2QjHCTgMVKt1Ds5TdHstXKTzJLIlhlrtrB/Gaely0WrTs3bl+CfaHCwcXlKtS0ptsweX1BuNZ1pXv/NuB1/YvwDgQYuN6eO4tA5amT6S1mNOHU+jORrAPb+F2ZME3zXgp8UksHaZpVpvMGDXs5vIU6rV6bZoOcmWyFU+AId4sYxLq0QUBb5wcME9vw2NXEYoXUQuQMCoYSfxYp2hx6q7UmYTaDWqOcmWqNQbRLJFvAYNidKL0YLrRieSW6sgkpNaYbXVAj/YG0Qt/8Cptra2srm5SUtLy1unZhQKBfl8nmQy+drawvMRgMlkwmQycXR0RGdnZ/Pnb9NmKpPJaG1tZW9v7yMNCh+5xJfbLfUnP3/ij0ajzejB7XZTLpefEeh+fs9NOzs7o1QqcXx8zM///M9jNBr5jd/4DT772c8SDAbxeDzYbDYMBgMqlQq5XP4Nd8jvwkTz9XV8eX6e7/3bf5tULodOp2J5ew+f045KqWD/+JS7w/0sbe2hMyi4PdzFzMIGfo8DmUwkdHzOxGgPiWyacqXK3dtdTD/exOUwYTHr2No9Zag/iEojJ50uMDnZzfT0DhqNgoF+P3Nz+zidOgrpIqGjGGPDAfYOLshkS0ze7WDmyT5yucDYcJDHj3Zx2vSSVsLuOV2tdvLFMqfRNOODfrYOLsgVyihqdR6vhWk0GtwflGYT1EoZQx0uZtdPsBo1eOwGVvei1PMllHIZZ+kyXR4TuUKFs0SO4VY74ViGRLbE7U4XW6cJcqUKfp2KxeM4pWqdBx1OZg8uqNYbz2grTHZKfEnXswyZrFTjmmyxNwFBmmr+YL1wBQiTQRuPwgnqDaiVKixHM1TrDUadRjZjWUq1OkMOA6F0gVylRrflA8bUFqOaSr3BWbaERiHHqlJwmi2hkYu49SoOUtKUsSTbeQ0OuqZUp1OocJQpUqk3CBglUr1cWWI8VcrEZrRgv9GJ5NYoiFxFDkGdgo7C+TOAAOB0OgHp+X2bSAEkZ2+321+re9BoNF76fm1tbRweHj7TTPK2YBQMBqnX68+koD9q6aOPHCi0tbXhdrv5whe+0PxZuVzmq1/9Kg8ePABgfHwchULxzJ6zszNWV1ebe26a0Whs/uHeRHMB79bw2jc6hfS1lRV++Gd+hmqtxlhPDzOrK0wM91CuVDg5v+TBrUEeL6+jlMtBXmNueYfOVi/5QpGzaJwHt/uZXdxi6yjE+GgHj+d2CPjsCKJA6CjKnVtdrK2HSefT3L/fxdTUNkajhpYWO0vLR3R1uikUqiw8OeBbJ7tYWjuhWKry4I7UeaTTKunt8jC/dIRWraDdb2XvKMZgt5uzaJp4Ms+90Raerp9QrtSYHGvlDx7tMtzuZLzXy8xqGKNeRavXwuJOBK/dgE6jYOc4TmfAyt5xnEYD2mxqTuM54tkid7pcbBzHyZeq3O/1Mn8QpVyViPKmlo5QyUUmO11M70ldbpOdLqau1vc7nEztRhGA++3SLMP6XpTJFhtTx1cTzldTzQD3gx+sR23q5noyaOPzO+e0mzTcdptYjEpcR7dcRtYuM5RrDYYcekJpiTG1+waddsCopt5oMB9JYlLJMCjlhDMlVKKA3yjpKAhAl0XbBIRus4ZoQ0G9IYFGNC8NtR2mcshEgUxF6kQyKp+dW4hcrQcdBr7FrUX2Ev953TIaCoU+lFKax+Ph4uLilYR314eq59/PbrejVqs5OTl5Zu/bfO51TfDs7OyNe99VeydBIZvNsri4yOLiIiAVlxcXFzk6OkIQBD73uc/xMz/zM/zWb/0Wq6ur/IW/8BfQarX82T/7ZwEpBPzhH/5h/tbf+lt86Utf4unTp/zQD/0QQ0NDzW6kV9lHieYC/mhaBn9U+89f+D3+yX/5LyhkMnpbWpjf3KS3tZVCtchFIsXkrUGmn0p1hRavm5mlNb71wTCRizjxZIbJOwNMz61j0GkIeJ0gQleHh1y+SOQ8yf07Pcwt7NFoNNDqFWxtneF0GrFa9WxunjE46OcskiCTKTEx0Ua5UAEaTIxJRWeJRtvMyvoJHa12SqUq9XKF8QEfO6FLsvkyk2OtPFo8pNFocG80yNRCCJ1GgcugZm7jFKdZi82oYTN0SZvXTKVW5/g8zWC7g0g8RyyVZ8hn5jhRIleqcr/Xw9zuucSW2u9jZvtMOvH3SkR5uWKFTzYH1wTutjuZ2osiFwXutNqZ2YuikAmMt9iZ2ZcG2rpcRmrVGgpR4LbXzMxxHLkAd3wWZo7i0mSyQ8tiTIooboKGTSFrTizfdktEePUGjN1gTB1y6Ald0Wl3W7QkChVihQrFag2rSkE0f8WGqpFEduQCtJqeTSVtJwvN9WFaGmrz61USADQaaOUiKpmMRKnaJMy7jhbGHDq+o8UGVwOTLzO/308mkyGTybx1pKBWq/F4PM8Q5d2064Pd8+8nCAJtbW0cHBw0n/MPO6WcTqebPEwfNXsnQWFubo5bt25x69YtAH78x3+cW7du8Q//4T8E4O/+3b/L5z73OX70R3+U27dvc3Jywuc///lnhk7+2T/7Z3zf930fP/iDP8jk5CRarZbf/u3ffuMf9m0ihXdleA2+MRTejUaD//t/+Q/83X/98xi1Wjx2Oyt7e4x0dRE6O2Nxf4PJW4NMPV3FYTFjMxnZPDhirK+LaqMi1RXG+5l6sobVrMflsLC2fYjWIOP0LE48nmXybh8zj7dRKeUM9geZnd9l5JZfSjmFLhgba2VnJ0I2W2JoyM3s7AHRcIzhfj+zC1d6zTo123tR+ns8RC8zXMazyOsNNvcvXuA/Guv382jxCItJg89lZmZ2j3afGZlc5OA0SV+rnViqwEUix3ivl52TBNlCmfuDfja2z6nWGzzo9TCzKYHAg34vU5uniILUnTS1eYZCJnC700X4LIlaLjISsPH44AKtQka/18KT0CV6lZxet5m5Q2nd7TIzfxgjl8jT4zAwd5pEKxeb086SbrOJpYs8cgFuey3MHEtAcddv5Xc2TjEoZIxf8RuBBA4LLwGHQbuew3SRbKVGh1l7VYQuPcOG+nwqqfNGV5JHVmE3WaABtJk0RPJlitU6Rynp9eto4ZowD2DSreeOU99Mh77K4SsUCnw+H+fn5x9KFKe1tZWTk5OX6h68KlKAD9LU10R5bwsK1ykpt9vN/v7+G/e/i/ZOgsK3fMu3NFMjN79+9Vd/FZAc4j/6R/+oKb791a9+lcHBwWfeQ61W84u/+IvEYjHy+Ty//du/TSAQeONnf5TSR/DfP1JoNBr83/7dv+Cnfu2X0SiV+B029k5OuNPXx9r+PpVKhcGODoqVEn6XA4VcxsHJGRPDfSxt77EfCTMx2sPM/DpepxWdVsNu6JSxwU4WN3aoNxpSoXlmE6NBQ1uri6WVkBRBlPKcnSW5e7eDxcVDSqUq9+91srISQa9XoZDLSaULtARsErvpSZxbwwH2Q1c1hokOph/vMdjp5N5IS5P/qLvNwfxaGLfDIAFJ6AKPw4DTpOXsMstot5uDsyTpXIl7g36e7kYoVWqSIttqmONIklteLdObZ8hEgYkeD9ObZ6jkIqNtTh5vR9Cp5PT6bcztnnMUSTIcsPH0WJpeDlj1LIfjWLUqPCYtKycJbDoVbpOW1VNpXSiUyZWqWDQK/GYty5EURpWcNquOp2cptDKBNqOKudMEKpnAqMfM43Ccar3OoE3H/BUgjLs+AIc7N8DhlsvI+lXNod+m5yRbJF2ucpIpoJIJxIoVTCp5M5WkFAWCRnWzK6nbrCbakLpzuixaQlcsq369qinEo5ELqOUy4sUqogDf1WKl36J55t56ncNvaWkhmUy+1X16XQMwGo1YLJYXmEyv97yqvfW6xfTg4KA5b/S2YHR9rdFolFwu93FN4aNu13MKr3O271L66L/ndVRrVf7aP/8ZfvG3fp2A040gighyuN3by9zmJnKZjKHOTmbX19EZlBRKJU4vYjwYHWR2eQOFTI7DZiKZztLmd1Gt1zk+veDuaC+Lq/tkclIr6vSjLew2I3abkY2tMIN9Ac4iCWafbvOpT/Xy+PHeMyR5ZrMam8PA+sYJbT4LqXSe84sME+OtLF/VGCYnOpia3UOpkGFSK3i0dIjVpMXjMLK6HaHVL800HJ0mGOpxcxLNUM5Jswkru+fSe4wEeXTVkfTgihxPJgrc6fNQLFZQK2QMtTmY3Ylg1Cjo8FhY2I9i0anw2fSsHF7iMKmxG9Qo6g08Rg1GtYKt8xResxatSs5ONI3PrEWjlLEbTeM1a9Eo5exG0wSuaSsuszh1KqwaJRsXGawaBQ6tgp1UCaNKTodVz8JZEo1cZPBK2EcmwKjTyPz5FTi4jTx5SVpp1GlkO56jWK3TY9VxnisjIBWHBSCaL6OTi9i1SkLpIjJBoMuqZS8tdQ/1WD+YW2gzqYnkyxSqdaLZIgIC6XINpSjwf2i302l+dkDsTUVknU6HXq9/6an/pj1fQG5tbeXo6OiFg9yb6gQ+n49CoUAsFvtQBHsAer0ej8fz2kL3u2ofg8JzptVqmzTQr7L/f0wfFcsl/uYv/Rz/6Yv/jS5/kFwhTyR+iVItMre5iUGjod3nY3F7m/62NnZPD0mkM1JdYXEVo05Le8DD4uYuwaCNeCpL9DLJg/F+Hi9sIZfJGO1vJ5VN4/NaUSrl7IfOGRttZ2fvTJptuNdDpVp5pvPI57OiUMk5PIwxMhzgcDdCMlXgwUQHs/NSYfLe7TamZvfQ65R0dbj48h9s0NVqR6tRsHN4SU+7g0SqQDSWZXzIz1boklyhjFoU2A3HpGG1kSBTKxIITPT7mF4JNzuSnmyccX6eo8tnYfHgArtRjcOkZf04hteiQ69Rsn2aJGDXIxdlHJynycQzNAQ4iufocBioVOuEE9K6VK0RTuTpcBgoV2uEEzna7AbCkSSRbIkWkxZREAgl8/gMarQKOYeZMla1DJtWyfpFBpNaTtCsZSmSIpIuMOY0shhNI78Ghyva7GfTStKeaqPBsMPA/pW053G6QLnWIFmqStoJChmnWanwHLwqPAO4ZNVmKqnLrCWUuibMU7IVzyEXBTQyge/y6tCWc5yfn3NyctLkGnubziKbzUapVHptpH59oLt+L7vdjlKpfKH4+6aUkFwup6WlhYODg7dOH92sU7S1tXF6evrGzMO7Zh+DwnN2TaL1JvW1b3T66Po6/nuAQqaQ40//k7/B9tkBA60dnMUuiWfSTA6MsHCwxVBHOw6LhfWDA251d7N/csJp7JJvu3eLqaer2MwmHFYz63uHjPR0cHh+RiqdY3J8gOknGxh0GrrafSys7pEp52g04PQszt07XSwuH1AqV7k/0c3Uo01y5Vyz86ij00mpUuHiIsfoSID1jVN2d875jk/2Mj27h0IhMjYc5NHcATarFrfTxNrmKQGvGZdFTziSYrjXw9FpklSmyL1bLTzdOG12IU0/DdEbsHFvyM/UyrNtqUa9ilaP1JHkMGtRygTUchG/TY9SLmMvkqLNZaRSr3N8maHbayZXrHKWyNHrt3AYTeM2qBnwmrnIFLnIFhnwmolmilxmS8+s+71mYrki++dpPumzkC5ViGSLdFh0lGp1wukCXq0CmSBwkMjj1qswq5VsXWYxq6V0UyJbRCMT6LLqWYxKzKgSOHwQLcxdA4XLyMrVENyATc9GLItZJcOpVVJrwGWhgkEhYtcpOcoUkQEBrYzzmjT21KKVsZOUogWXvEEkWyJfrXMWOcd7ucfB6iJbW1uEw2EuLy/Z2dl5ZXvo86ZSqZDJZM90Bj1v18/mtRO/pr64TgVd29t8XjAYJJlMUq1WP5SW87Wqm8Ph+MjVFj6yw2tfL7vmPCkUCphMppfueRfSR9fX8fWuKcTSCf7Uz/4NFvbWuNczyt5pmFKlzL2+YabWlrAbTBj1Glb29pno72d+cxOAif5+cuU8XqcNURDZOz7lzmAPi5t7VKpVvvXBXb4ytYzVrMdqNrK2dchAdwtHJ1F6fO20tjiZfrSJXC4yNtLOzOw2ToeJdC5HNgb9Az6Ow3EymSKDAy6Wlq/mCu51ks8W0euUtAbtzC8d4XWbEEWR3YML+rrdnJwl0RlS3BkK8HT9RBLPud3G1EIIgPujLc0CtFqAL6+dYNSp8DkMLO5EnuFFCjiNVGp1IrE8HdUahXKVWKZIn9/KSTxLOl9muMXOXiRFrlRhtM3B5kmCYrmKVS4yFZaG2MZbbKyeSOuxoK053HYraGXjNEWxWmPYbyWezJEoVhh0GjlM5smUq3Tb9EQyedLlOm1mLfmKRJbnMahQiCLbl1mShQqjrQ7WYjeZUV/UVLh9I3IYsmlZi2epN+A0kUamVFGqg0FsIDZqRHIN5NQxCDWO8wANvIoGh1ct+gGNyEmhTh0I6JT8+VEvdr32mRN3Pp/nyZMnJJPJt55B0Gq1HB4eEggEXpqvfxk/ktfrZXt7m8vLSxwOB/B2swfX4j1HR0dvHSnc3NfR0fHWdZB3xT6OFJ4zuVzenIZ8lb0L6SP4+g+wncTO+e7/+a+wsLfGRPcwT3ZWaPf4GOvq49HGMm1uH7V6nXDyjPtDQ8yur6OQy5t1hVwlS6VaI3x+wf2RfubWtmk0Gtwe7KVcK+N1fVBovjXYwd7hKZlcAbtTx/QVxUV/T4C5p3sE/HZkMpGDwyhjt4PsH1yQyRSZfNDN6to5MpnA7dttzDza5fz4Eq/bwurGKW0tNiqVGuHTBKODAQ6OYqQzRQwaBcdnSQkQxqUuJLlM5Pagn5nFQww6JV0tdr78cJuBNgd2k4aN0CVBlwlRJhI6S9IdsJErlInEsrQ6NSxvRRAFgVvtDg7OU6TzZW53utgIx8mVKkx0u1k5vKRYrnKv28308jEahZx77Q6eHkkDbffaHc3htrttDpbDCYrVGnfa7KyfJljYOeeTLTZ2Ylky5SojLhPhdIF0uU67UUmsUOY8V6LdoqVah6NUAa9BhUouItRq6BUiLq2C9VgWhQDtejlPz6UIoVsrNAGhU11nJZaX5g50MpZiBXQysCkFBLmMbF1EJxewaVUkGgpEwCWrc1qRXEqPRcfxFSD023T8xL027HptU8CpUqlQqVSQyWS43e6mBsKbnHStVkOn01GpVLi8vHzpnutn4iZgXM863Mzxv22dIBgMAryxlnF9fTff02g00t7e/sbfe5fsY1B4ib2JKfVdihS+XtexGznkr//yT7F1csCD3lvMbi+jVijxuuzMb6/TG2wjlkmRyGWwm00cRSIYtdpmXaG3tZVQ5AyrycDkrUFmltZRKxUMdLYyt7pJsZanWpMKzROjPSxvHFAsVbg/3svX5pZxOU0E/HaW1w6lzqNckbNIgonbXZxELykWKzx40HWlqyCju9vF3NwBHreJcqmKXCbS1+0mFs9xEcsyMdbK6uaJRL890cHMkwM6/BbujrYw9fQQrVpBf6eLudUwNosWp83A2u45frcZh17N/mmS7qCNTL5EJJZlqMPJyUWaeKbIWLebk1iRTK7EWNDGcuiSYqXG/V4P83vSzMKDXi+z25GmzsKj7YgEDkHbM5PMzXWHk8cHF9TqDR50OHlycEWF0e6gXqpSqtW57TWzdpEmX6nRY1Jykq2QLlXpMCo5zxS4yJXwakTyxTLHqQI7J1HU1DnMlNGK4NHI2M1WkQN9ZjXbeSnqHHcZ2C2KV2sjR4U6lQZolAqKDZFctYFVJUcll3Ger6AUBVwaOec1yRl2mTVsJaSBsTsuAz824kMpSA6zXq836Wau9c69Xi/n5+eUSqU3gsK1Iw8Gg6+dP3gZ31ggECCVSn1oHedrzqPj4+M37v2oq67Bx6DwUnsTU+q7VFP4eqSPlg43+K7/5c+RLqaZ7BtjevMpZp0Bn93FXvSQ4Y5uDs/PSOeyDLd0Mr+7SWfQ26wrXM8rpHM52ltcTN0YYFva2qOnLcjOyTFKpZwHt/uYXdxCEARuj3QxM7+JQa+is8PN1s4pg/1BaXYhkeXB3R5m53ZY3z7iE5+Q6C5MJi1ul4H19TPa2uzU6g2Oj+N4bfpmVPBgooPZhRDVal2adJ7dQ6WUowQeLx9hNmrwe8wsb53hcxlRKxXsHcUkGoxCid2dCMMdTsLRNIlMkdu9XjYPL8kVK9wb8LG4e06lJnUkbe99ILBzPbMw2edlelMS27kpvDPZ62HnUOI0mryaZAa412ZrTjjf9puak88jbh2P9i9Y2T6l3yAyd3pFhGeSs5MqU6o36LeoOM5VyFUbdFs0ZGoCyUqDVrOGbF2O3aDDplZg06k5ytfQykU6rDo2kkVEYNRpYP5cKvxKhecM9QYM2vV89SiOKEhcReV6g3ixik4hYlErOCtUgQbtRjU7V4Xn72yx8iOjATQqiTNMpVKhUqlQq9XN9TWRpM1mI5lMvjUoBAIBEonESwWxXhVxXKeCrqOFDzMdDXB6evrGaOGjrqUAH4PCS+1NswrvSvro6xEpTG/N8yd/9i9xkY6j0SiZ2VzEZbJh0hnYPglhNxpJZjOUymUmegdZPtzFZbZSofLMvEKpXObe4CArh7s4rR8MsA33dHB0dk46m2ewP8j03AZajYr+riBzSzsEvQ4EUaTSKDM+2s727im5fElqVX28hUolZ3SolXq9hstlxGLWcniUpLPTSTyeJxpNM3GnnaWnB5RKFSbvdjA9uydJcV5NOhv0KjranXzlq5uM9nox6tVsH1zQEbRRKtc4OU8x1O3m9DxNPFXAbdVRrdXJFyvcH/Qzv3UqyXUOBXi0JrWoDgQMTK+EOTiO8+1DfqY2ThGAe92StoIowHi7vbkeDpiZ2jzjIBxnzKlhak+itui1Knl0EEMABp0a5sJSOmfMZ2QpcsVO6jKhVEsNEQ+CVtZTVerAqF3LZrJEudbglsfEYVpiQ+1zGIgXKhILaamCKMBxpohZJceplTqDVKJAr01SYBOA2y4jT6/A4ZbTwNpllmylhlurIFGqka3UrobaZJznyyhFAbu8wX5airB/sNfDnxsKoFIqmySToii+4KxFUUQQBLxeL6lU6o0O9Nrhq1QqPB5Pkxn5ZXteZi0tLUQiEQqFwltHCtf7rFbrSz/v+b0fRwrfhPYmqot3JX30x11T+Pzy+3zfz32WbDHPROcIX9uc5UH/CIIochg95X7PKHN7awTdLkY7u5ndXMVndVCpVZnZWuKTt0aZ29xEEATGenp4tLoKQgOPw8bByRl3BnvZ2DukUCxxf3SAg7MwJqOOgNfB8sYB3e0+MrkCkWgCuQbWt8KUy1XuT/Qw9UgaZuto87CwtE+pXpKong8v6eq0Ew4nSKXyPLjfxeyTfS7O03z7ez1MPd5DrZIz2OdjdiGEzarD6TCxvnVGS8CKWavk6DTBQKeLaCzLZSLH+MAH5Hj3R1uYXzvBqJAxOSQNqzUacG/Ax9TKMQJwq8vB2nEGUYCBFgsXkRhyEbqcGh5tR1CI0GHXML9/KdFWuPUsHydRyQX6/GZkohylTGDYb2EzXm7SXKxGC8gEJCbVk7QEMu0OHodiNPJlHgQ+YEkdtatZvJRqAHd9ZpYiKUq1OqNuSV8hXarSbdOxdJqk3gC3TolaLhJKF9ErZASMGtZjOeSCwKjLyNOoBAh3PCaeRjM0gBGngblImnKtjlunolKvEy9W0CmkuYXLqohAg78yEuB7u1xvfUKWyWSYzWZkMtkb2zdvOvyWlpaXnt5f55h1Oh1Op7NZw/gwxeO2tjaOjo6a9Pmv2/tRto9B4SX2NqBQq9W+4WR0f5zpo998/L/z0//7P6fRaDDS2sfs7hJd7lZkMhmRxAWTfWPMbC2iV2lQKEUWdjbpDbaRymeJZ9I8GBimVK2gVamaPEidPj/5fBG9Qc390QHm1rao1+vcGeplZnGNZC5Fi9/J1l6Yod5WTiIxEqksk3f6mZ5bZ6A/wJ2xTmZmt7BZDTgcJtY3j+nu9LIXOkEQBO7cbmf/INaU6pyekSi179xuJ5sqYDRoaA3aWVoN4/NIEqB7oQt6Ol2k0gV2tk4Z6/exe3RJJlfi9qCPpxsSOd54v5uZK16kUjrNo7WwdJr36Xm0doJchG6/kac7FyjlAt1+M2uHCc7Pc/R4zWxHCxg0Crq8VnYuChi1Sjo8FrbOshi1StrdFtbCSU7P0vS4TSyFE+iUMnpcJuYOL9EoRAauNJyVMoFbQSuP9i8QBVDX6+zGJRGZ+wELi5fSCf1B0MrjE8nx3/VbWDnPXIGDieN0kVihTJtBTanWIJIr49AosagV7CbzaOUivTY9y1eAMOY28eTsetjNxHI0w0EyL/EjFStkyhI3kkYuzS0oRYHvUOcYNnw4t3JdX9DpdGQymdfe0zdBwWg0YjabX8j1v6lg3draSjgcplKpfOhIQaPREA6HX7v3Y1D4JjStVvvG7iP4xpLRwR9fpPDLX/lP/JV//3c4iB3SH+ji6cEag4FuzpJR9i5CTPbdYmpjAavehMti56vrs9ztHSIUOSVbLDDe2cvU6iJ1sYLP6WRlb4+B9nYil3Hi6TRqjZyZxTVUCgVD3e08Wdkk4HEhCDL0ehXjw51s7YXJ5YtM3uln6sk6GrUSq03Dk4VdfB4rGrWSvf0IQwNBTk5jJJI5RkZ9zM0fUKs1GB9vYWp6G61WyUC/nydz+5wdX+Kw6djcidAasJIvljk5S9LdYSd0fEkyVcCkFbmMJSmVawy0m5lbldJBI9125tcjyEQY7XHxdOOC4XY7wx1ONk+y6DUKeludbIXTmHQqXCY1m8dJbEYNBq0SlUKBw6jGbtSwHo7jNKmx6lVshOM4TGqsejUb4Th2oxqlTEApCNi0yitqiyQmjYKgVc/ySQK9UkaXy8TCURzVNWdSKEa3UcNdv5WZY4kivt8oe4ZO+3E4Qa3R4K7fymo0TaFSY8hlYvU0SaoksaFyI5Xk1avZiGWRCzDsNLBw3abqMTEfSTWjhVBK0mRw65RUGg0uCxV0Chl//34n94KO1zrNl9l1WkmlUlGpVF7bwvm8w7+eVr75HLwJFK51nJPJ5FvXFK4L1+3t7U221pfZy1JSH9cUvgnsbbqP4BtDRvf8dfxRrqHRaPBP/r//gr/zm/8Yq86Mw2BFLpMx1jbAzlmIXLGA3+Hi+DKC1+pAp9aye3bEeGc/iA3KlQpDLR3M727isthI5FMcnZ8z1t3D7mGYbKHA5PAwX5qbpSvoo80vTTR3tfjJ5QpELuOo9TKeru5Rqda4N97L1JN1jAYdLX4nM0urdHd6KVeqhE9jjI92sLUt1RgmxjvYPjhGFKG3x8H8/CF6vRK7XcvS8hFOh45MOodIhdaAiWgsSyJZYLDXyV4oTqlU486tAOvbMTwWI/dHg6ztJ6Xaw3CApe1L1Co5Qz1eFrfOMehVWDUqlvai2IwaXFY9q/tRnBYdJr2K41gBj02PWiVnN5xAVZU6oA7O0wTsekRBJBTNELTrkQkioaj0c4VMxkE0jaJSQ6NSsHeRwW3UYNaq2DpPY9OrcZt1rJ0mMaoVdDiNPD2KoVHIoFhhNhxHJkjkd+tpqflhssX2AYV2i+2KA0lSaduKZdmLZ7nrNpEqVrnIl3HrVOiVcg5SBXQKkQ6LjuWr2sKY28Tcc9HCdDhBt0VLslQlU65iVSv4h5NddFl1+P3+ZifRq+65crlMNpslHo9zdnbG4eEh+/v7pNNpDAbDa/P2zztdh8MhRbM39FXeplbQ1tb2VjWM6/e7Bg+Xy4Uoii9VcLzeK5d/tMe/PtpX/3Wyt+k+gm/8DfBHSR/V63V+4n/7ab6wOIXH5EQuk7MbDfHpvla+tPgYURAYax/k0c5Tvq33E6zu73IaP+N+7yiPtpYYbxlktLOHhZ0NvFY79UaD3dMjPj32Cb40M0+DBncHB5haXsZuMeP32vnKoyUGu9oIhc/J5gtMjg3ylbmnOG1OPE4rj+Y3sVkMaNRKNnfDtAecyOo1Li7T9Pe4ebq0T73RYKDXzez8HkqlnIGBFpaXz7BaNWi1Ko6OknS0O4gnciQSBUbvdDG9eEixVG2qsDUaDR5MtDM9u48oCiiA6eVj1Eo5Pe0OZq+kNj0OI4sbp9gtWgw6Fe/P7NDZ46VQrrJ3kiDoNlEqVzk6T+O1qilWqsTTRbr8VvZCMSpGDT1eC9Er9bUen4VoSlp3ey1cpgvEs0U6PWb2wnFEm4E2m14aPotl8Vt0NGiwG03jNKjRqRSsnyYxa5W4zVoebke4MxykAjy+Aoduo5ypww8A4Xr9IGhj5jhOA7jlMRNJFUiXq7SaNOTKNS7yZSxqBUaVnK14DoUo0GvTPxMtXIPDsNNIplSlWK3j06v5O3fbMMggk8lQLpfR6XSsra01eYquv0qlEpVKhUajgUwme0G21ul0YjabWV5eplgsolarX3rf3nT4giA0tRY8Hk8zen5TBHCt4/y6w9+13QSZ6+no/f395ue9au9H1T4GhZeYTqd7Y03hXVA++8NGCpVahb/26z/Bb8z9Ft/W8UlWj3c4i5/yoPM2s6GnaJVqWp1+5vdX6PG0ky6liaZiTPaNMbWxgF6tpS7UWT04oMXpJpHNkM7neDAwQiqfQSaK9Le38Xh1DY/NRr3RIHx5xkB7kK39MJVqlaHOIFMLq6gUcrwuPU9X93HajNTrDcJnMfo6fewfndPXamRivIPZ+T1kMpE7Ix08WdjFZNLhcZkxGLS4XXrqdYFwOMngoJ+DgwtyuRITd9p5MrNDQ6PkwZ02pp/sIwhIXUiz+6iUMvq6PTyc2eXOe91kCmWWNs9wWHXoNEq2Di7wu03U6g0Owgk6AlbcZh0P18L0ttiJxLMkM0UG2x0cnCbIFasMdTrZP0mQK1T4rtEg729HyJeqjLQ62DlLkC9VGW61s3uWJF+qMhi0E4qmyBYrfGe/l9lwklShTKfTSCJfIpYt0WLVUa7VObjM4DKpUSsVbEZSmLVKTKLAF08SaOQiPXYDi5EUIjARsDYB4b0WOw+vIod7AStPrtJK3zscYCch8Rt5dCrqwGGqgF4hw2tQs3IhRQuDNm0TEPpMClaiafbiGb7da+DbhChPp6ScvlwuR6mUtJ4TiQRqtRqNRoPZbH7G+V9TVTxv9XqdSqWCzWbj+PiYrq6ul+553un6fD52dnaa0ptvMwR3TUORSqXeSsf55vX6fD52d3efmY6+uVehULz2s991+xgUXmIfFaGdPwww5UsF/uKv/V/53bUv0ePqJFVKEU1fMtl1h6mdJ5i0RgaD3cxsP2U42MtOJESxXOa9/rs8XJ/HrDVg1ZtZ2F/nXtcYi7vbFCtlhls6mF5bwqI14rPbWNzewWuzkisWSeVyuNpNHB8mqNaqjPV3sbC+g0mvw2kzU5MLdLV5iSXSxJNZJkZ7mF/ZoVarYzCrmflqCLVKQW+PjycLuzgdJolmYvuEiVEduXyFTKbE2K0WVtfClMs17t/rZObRLgDf+alevvD+NkqFjME+L7MLIQwGNQGPmcXVME67AYNawZO1E1q8ZsqVGqGTBF2tduLJPLFknoEuN0enCTSGDKNdbraOYhRKFcZ7vKzun1Oq1Oj26dkMXVKp1pno83F0pb420eVmYT9KtVZnosvN0/0olVqd2x0ulg8vKFfr3Gp3sn8cJ1WsMuSzcHCZIVuq0us2cZ4ukMiXabPryVfrHMayuI0aVAoZX1k+orXDhVohYzGSQilCh0nFo6aO8weAMBn8IK004tSTz0uSnD6NjFSpTLbawCADNTW24zlkNPCrBVZiUtTcZ5CzkZKIIoesWv76qA+jVtN09teOs16vMzU1hd1ub0ppvo3dbE/d3Nyko6PjBef+sihALpfj9/sJhUJvDQog8ShlMhkSiQRWq/WV+57/TJlMRktLC/v7+y8FhY/nFL4J7W1B4Rs9wPZhgSlVSPPn/h8/wu+vf4UhXx/HiRMWwivcax9jaucJdp0FvUJLsZSn393BeniHYrlIj6OFi/gFFq0RpUzJ/nmYPm8bpWqRYqXMUEsHy4d7WHQGrEYTWp2W/rY2MgUJEB4MD7O8f0B/V5Cx/m4W1ndw2SyYjXp2Dk+oi1Wy+SLxZJb7Y73MLkpdShOj3bw/u8qt0VZaW5wsLocI+O2IokDo6IKh/hZWN47QapUMD3lZXDqiXK4x+aCLmUe7yGQiE3faSVxk0OtUdHe6WFg+xm7V47QZWN+O0OK3IpOJzD7aY7DLRTpb4uwiw1C3h9PzNLFknvEBP7uHUneSVi4SS+UplCqStsLOGaVKjftDfnZOs1SqdR4MBXiyecLG7jnfMRxgdidC9Wqq+cluhEqtzv1eDwv7kkzn3W4Py4eX7J0k+M5eD1uRFNlSldGAlcN4lkS+TJ/HTLxQ4TxdoM1moN5ocBjLYteraNEp2bzIYFDKCBrVbCRKyAWBAaua6SsJzwGTrAkI/UYZy9Es88cJ2nUyLkt1stUGLo0clULORQV0cpEOq57Dq+zKmNvERkZqxfyBHg//+v94m4DHjclkQqPRPOMIRVHE5/N96IIzfNCeqlAoXipp+SqHf61fkM/nP5QgjsVieSO99cveLxgMkk6nXyiKf9x99A7YL/3SL9HW1oZarWZ8fJz333//j/yeb0ofwbsTKTzP+lgqlchkMsRisWYRb2dnh/fnpvj2f/69fH7ry9xy9bNxtkOxXKLH2kY6m8Kls0MDTlIRFCo5G+f7CILAcLCXzYsD7HYLSoWSaDrOvZ4Rts4OOctEGWrpYOVwD7fVjl6jY+80jMdpYe/khEw+z4OhIaaXl9Gq1ajUMubXtgl6pNPj4ek5t/o62Q4d4/daeXC7j5mFTZQKObcGOphd3MZhNWEwq9jcPqH7iu4icp7kzq1OtrZPyRdKDI/4WF45vSLE62JqegeNRsHQYIDZJ/uEQxe0Bm2sbpwS8FpQqeTshS7o7nCSyRY5O0/RHrShUytJpAvcGfSzdRAlVyhL+s0bJ02lttnlY4I2PZPDQR6thqnXG7w3HGRmRZpfGO2wMr1yTKMB740EKVxJTr7X72N681T6eb807VxvNJjs8/F4R6K/uN/jIZMpUK7VuX1FkFco1xjwGNiPZUgVyrRZ1ETTOaKZIm6tnFKpzMbuKWYF6GWwmyyiFqHFoGAtUUIGjLsNrKWuitBBG+vpGg2gy2FEq9FQqjfoMGsp1uGyKBWObVoV21e1hZudSP+X0SA//ake5G84ift8PhKJxCv1kV93TwuCgM/n4/Dw8IWa2atAQaPR4HK5mp1IbyuIY7fbicViZLPZV+57WZ1AoVAQCAReAJTno4qPWpQAH/H00W/+5m/yuc99jl/6pV9icnKSX/7lX+Yzn/kM6+vrTRKrP4y9S5KctVqNcrlMpVJ5pmhXLpebzJLRaLRJMAYf5Havv2KlOH/98z/BYeqYce8ochTIBJFBfy+L4VU+0X6fSC5GPJ+U0kjbT+hwdqJRqlk62qTb08ZB7Ih4Jsv93lFmNhdRK5S4LDZSsTxei51qtc5x8pw7vQNsnOxTrlS4OzjA9MoKZr0ep9XC11aeMtTdRThyQSKd5d5IH7MrUlRgdej5/c8voteqaQ26WVjdI+CRaCsW1rcYGWpld/+MXK7E/YkeHj2W6JYn7/dycCQR4g0N+pl5tIPJqMXjNbO4dIjXa0EmCujVSjrbnSQSOWKJHMP9PnYPLsgXytwZbWVx7ZhhnYr7tz7QbJ4cb2NqXnro3xtv4+HVWi3Al5YlJa8HQwEeXq3v9nt5vH4KAjwYDPBw+RinVceDPh8P1yWq54kuJw/XJZqL8TYrU1f0FyN+AzNbZyjkAoMdVuau6gEDTg0bUYmptN+pYy9WoFSr0+0wEMkUSZfqtOg1tDgsPDlNYNMqMShE9tIlqc7gMDB/VQ94cCN9dJ1KuiMI9Nv07KfyFKt1vHoV1XqDo7TUieQ3aJqdSP/jZBc/NOh/q/tWpVLhdDoJh8P09PS89f1+3Z7qdDrZ399v1gmu7U3TyvPz8/h8vreeP7iejA6FQi+oN97c97LTf0tLC++//z65XA6dTgdAtVr9yEcKH2lQ+Pmf/3l++Id/mL/8l/8yAL/wC7/A7//+7/Ov/tW/4md/9mf/0O/79UwfXUv73XTuL3P411/Xn3Ht4BUKxTMOXxRFgsHgM6/ffCC2L3b43H/+Cc6yER60TTB9MEufo5sOZyuL4VX63T3sXOySyme43zHO1M4TLDoTAbubP1ibZTDQzf75Mflyge8Y/ha++HQGg0aPz+ZkKbTFJzrHebq1R7ZY4MHgCNOrS8hlMj556w5fXXiK22ZDpVSwfXTMcFcnWtQk0lkmx4aYWliRUjxDfXz5yTwBrwu1SsXqZojOVi+JVIZYIsPt4W6qWchlS7x3v4+H05uIosDdO91MzWyi06oZGvKzuHiMy3VVb9g8pb3dSSZT4PQiQ3uPh8h5imyu1ASBSqXGgzvtzFx1JGllIks7Zy8AwoNbrTycP0AUBSaGgnzp4TZ9t1rQa1VMrxwjlwkMttl5vH6KTBTo9huZXg0jE8GqFTm/iCEiTTjP7kQRBBj0GZkPSfMF421W5g+kGsDtdid1rQaIMdnlanIg3Wt38CR0Sa3e4FbQxuZZkkKlRq/bRCRdwF2uEDBqqAsCobTEaOozalg8S6EQJXnO6aPrwrONh1egIzYaZMpSJ1GHWctFvky6XH2hE+mffGsff6LT9aHudb/fz+LiIp2dnR/KUYqiiEwma9JYvC0omM1mdDod6XQas9n8xs+5qeM8MzNDV1cXKpXqlfueN41Gg9vt5uDgoAkobzsl/S7bRxYUyuUy8/Pz/MRP/MQzP//0pz/N9PT0H+m931an+TpSuKYDfpVjf97p1+t1BEF4xrlfO3uTyfRCq55CoXhpGLq3t0elUsFisTTD7Hq93mSifHq6xA/++v9AvJDgOzq+gy9ufxWbxkKpViabzTDqH2Qjsk25WuFbej/BVzZmcBkdqORK4sUE422DrBxvUa5WuN99i3wlj91owajVsxneZ6Sth8tCimyxwP0BCRC0KjWd/iA1qrR4PBRLJQ7PItzp72NpZ5eRtp4mIGhUSrrbgsyubOB12Gl1Onn/0TqDPa1S22quwP2xPh4/3ebuYB+T9yRAUCrlDPYHeTS7jdWqx241oNYocDp1CAIchC7o7/cRDsdJpwvcHm/jyaM9lHb9MyDw3t0OHj7eA2ByooP3H+1y75M91ICp+QPkMoH+DgfTT0Mo5SLtfhOPlg5RKkS0lHiyEUOtEPDatCzuXqBWivjsOjaO02hUMtrcJtYP49we8qNvNbIUukAlFxlodbCwF0UuCox1uJjdiUgUFj0eZrbO6G2xMdntZmpXEo2f7HQ113fbHMwdSuAwGrCydZ6iUK6RTuQQDVqOU5LIjliXisV6hYw2q54nJwnpMwLWJiBcRwvf3ed9IVqoNRocpgpoFTJ+8dODPPC/uhD7KjObzajVaiKRCD6f761/77rg7PF4ePLkyTPtqa8Dhev21LW1tWeA5FV2nRYyGAxYrVaOjo5e2vF0HVG8zNra2p4BlOejio/TR/8d7fLyklqthsv17OnF5XK9crDkbe16TuH4+JharYbRaHzB0efzeXZ3d9nZ2Wn2Xoui+IJDV6lUGAyGF075crn8lTfMTbCBD5Skrr+/+d9qtfoCF4sgCDw8muIv/7/+OvFCgnuBCXLVHB6DG5lMxn48xHd3fpovbHwNEZHxlhHKjQotdj/Fcomj+An+Dg+re/sSLUXHMDPbTxnw9aBSKNiPHHOna5DF/U0qtSpjHUPMrC1h1ulxWe0s721zt2eYVDZLMpPh/vAQj1ZWAVBp5czObmDS6/A67Sxt7tLm95DLFyjWiowPdbK6dUipVOG9iQEezq4jigJytcDUl7cw6NUEgw4WFvfxeizIZDK2d8+4M24gn6+Qzea4dauVjQ2JJvv+vU4eP9mXdJUHevjitNSRNDbk5eHjPWn4rdPO1OweCrlAKZ3k6WEWtVLE7zKwvB1Fr1XgtuvZDCUwGVQ47QYOjrI4TFosRg3bxzGsRg12s47t4xh6tQyP3cj6YRyzXk0pXyaUyGPUKAg4TSzsRdEq5XR5LczuRFDKRYZbHcxsnSEKYFIpCF9RWEx2uF4JDvOHEp32kN/C/kWGEbcZUYRcuUYkX8UoB6dBzcp5CpVMYNBlYuaqK+nmDEMuX+KiBsVqnXazllihTKpUxaZR8MufGWHAYfhDPUeCIOD3+zk+Psbr9X4oBymTyZrsqTfbU99UL3C73ayurr6VBOZNB97a2srS0hLt7e0vnPRfN3tgMBiw2WyEQiF6enq+KQrNH1lQuLbnb7Q39Ry/yn7kR36EnZ0dotEoR0dHZDIZBgYG+P7v/37+6l/9q884dI1Gg0qlwmQy4fF4mq+9bpDtbR39m/6d14U4QRAwGAxcXFw0I4nrPb+z83v8uf/6lxiyDdNqaeHR8Sy33CPUGlXOkhEetN3lsnCJSqak09nO3OEidwJjpAsZErkUk10TTG0/4V5wgkKpyJO9ZTpcLZynLjAprdzvG+XR5hKiIDLRPUQtL2DVGzHq9Wwdhxju6GYltI1JZWWwfYSHS0so5HJGurp4uLjIeyO3OYnE2Ng/pK+9hdPoJalsjo6gn+W1sMRuekcCBJVSwUBPC+/PrnLvzjCXFxnW1o9pbXGQzRW5PEvQ1+NldS2ESW8iGDCztHRIvd5gcNDFzFUkMNDvZH/3FFGE/i4nCyunqJQyOtvsrF1NLPu9Fp4undM5HEAURbZDFzisOgw6NbtHMdwOAyqVgp3DGF6HgRa/hZm1E7x2AzKZyPZxDK/dQK1WYSecwGXVoVYqWNmL8qnJbsKpPGtHMaw6FQ6zlqXQBQa1ghankbndcymKCNp5vB3hvfFW3GYtU3svAsJk5wc023da7Swex6nU6jTyJWIFSVPBb1RTKpXZjecwquT4TVrmT5PSDIP/gxmGyaCN9w9j/MlBP1UglMxTqNYJGNX86z8xQotJ+6Geo+fN4/Gws7NDOp1+pZLhy+zaCT/fnvqm4TBRFNFqtW+ldnYz1WOz2VCr1ZycnLxQj3xTSqitrY2FhQU6Ojo+BoVvpNnt9hfG2wGi0egL0cPb2K1bt5iYmMDpdLK9vc2v/dqv8Xu/93vNAtLzls1m0Wg0GAyGpkOvVqsf2slfr29+Pf8z4KUPgsPhYH19nUql0pQR/fXl3+Sz/5+/hlKmxKaz8PtbX6bX0cNe4gCDzMx77fd4uP8It95Fmz3I8skaQ75+1iIbWBR2+rt6mNp+gllrxKDV8mj7KQP+bo4vz0gXskwM3eJ3Zh+iVqjoDbQzu73C7bYhaDQIRU6509PP4t42lWqVT4118bvvP0KnVtMR8DO3sUHA5UShEjkInzHa18nW/hGFUpkHtwaZfrrKWGc/QkNk6sk6eq0Kt9PCwsouDquBci3H7n6EoM9M9CJFPl+mt9vF7l6ESrXO2JCVqYdS0XfiThuzcyFkMoHxsTZmn+yj1SmZuNvFo/kDTAYNXo+Zta0z7FY9JqOGje0IHpeRgNPEV+b2CXjM1Gp19o9jtPmt5EsVDk8TtAesZHNl6qUqHT4r6XyJ01iWdp+FbL5MNFHEbVHTAA4jSUmyM19mL5LCY9GhkItsnSSwG9WYtCpWj2IYtUr8Nj0L+1HUChn1QoUnlwlEAe60OV4aLTzocDKzH6XRgLGgjacHF7R2unHpIZ4vEyvVsShFLFoV69E0aplIn9PIo/AH/EjXhedqucpOpkS10aDPpueX/8QwDu3LUyYfxuRyOV6vl+Pj4w8FCiDd82azGblcztnZGR6Pp/nz15lKpSIej5NOpzEaja/c97JJ5b29vRdkPt/k6C0WC3q9vplZ+KiDwke2JVWpVDI+Ps4XvvCFZ37+hS98gQcPHnzo9/vsZz/LX/pLf4nv+Z7vYXh4mFQqhUqlekY68Gb6SBAEKpUK1WqVWq32AmvqdbFMJpMhl8uf6Qi6FhdRq9UvCI4oFAoUCsVrOeivTaFQYDKZiMelh/wXZ/8F/37xV9EptbRaWli9WGPEM8hh8oh0Kc2Qr4+H+49w6h1olGrkcjm3W0bZiuxQqBQZCvYytf0Ep9GORWdi/niRsdZB9iJHpAtZJnvH2b88wqjV0+b2s7i/QbevlVAsTLFa4XZ3P/M7m1RrNe71D3N8eYrFYMBjt7O8s0ubx0Mml2due5WhzhZWtvYplMoMtgeYfrqKXCYiilXml/cwGzRYTDp2QxGCXqkLKRQ5Z3gwSDSWI58vc/9uD1s7USrVOu/d7+X0PCmJ9Yy3MjsXQq1WMDQUZPbJPiajhpaAHRngtBuwWnVsbJ8906La1mKnVmtwcnhJd6uDXL7MaTRNX4eTeKbAeSzLQKeLy0SOaDxLMVsgWyxzkcwz0ObgMpknmsjR22Ijk69wHs9Jkp3FCtNPQ9zpdFGr1zm6yBCw6VHJ5exFUjhNGmwGDevHcUxaJW0uE9PrJ9wO2CTyuytm1HvtziYgvNfpYnpPAoR77U4Wj+MUKzX8KhmnmQKxQpkWkwah0WA/kcOkktNm1fH0TIoW7vmtz3Qi/f52BK9BxT2vmV/73lt/LIBwbdd8SG8jZ3nTrmsLfr+fw8PDZnT9Np1FZrP5lcps1/Z8BODxeKjValxcXDyz702OXhAE2traCIVCTQqPm6991OwjCwoAP/7jP86/+Tf/hn/37/4dGxsb/M2/+Tc5OjriR37kR/5I77u/v8/R0dFrHb3BYCCXy73W0d8sFCsUiubvvs7Rf1izWq1cXl7yU1/7x/zEl/8+8WIMu9bOxsUmXpOHdClLuVpmInCbSO6cgMWPTJRxED/EY3awcLRMA7jdMkIke07A6pVevzimy91GoVKkVClzr/sWU5vzxHJxgg43G8d79PnbCV9EuEwnGG5rY257HVEQ6Pb4ebS+zGksgkGjZjccpt3jJhKPk8xm6fR5KVer1Bt1bg90s7p/jF6roactyNbZMS0BFzq9luOzOAPdLSTTeeLJLJ0dPhpAsVjhvft9zDzeAhrcv9vDw5lNTs9j3BrzM7dwiMmooa3NweLiIS6XCatVz8bmKeVc8Urr+ZLOdmeTObW/x0M8niV6mUElF4EG8VSe0T4fodMkqUyRsX4fe0cx0tkS4/1+NvcvaHWaGOv2sHeSIJ0rMdrt5jCSIleq0eM3E75IE08XGGhzoJUJRFMFurxm8uUqJ/EsLQ4jMlHk4DyFy6zFcsWeatIqMYjw9CiGSi4yGrDxaF8S4nnQ4eThDXB4tB+l3mgw0epgbjtCowG9DgOpUpV4pYFdLceiUbJxkUEjFxnxmF8aLYw7DPzynxhBr/zjTSDo9XpMJhOnp6cf6vdutqfm8/lmSuhNJ/FarYbD4SASibySmO+6GePmc/gyHefr93vT8+p0OpvX9VGPFD6y6SOAP/Nn/gyxWIyf+qmf4uzsjMHBQX7nd36HlpaWP9L7/tAP/RA/9mM/1ixwveyGsNlsHB4eNk8zf9zWaDTIlrNE81Eu85dEchEy5QyHqUPqjTrrl+soZUrmTueIZCJY1DZaTEGSpSRiTcn9wD0eHT/mPd8nMKtNzB7P0WfvpVqrcpaOMNl+l43oJmq5ig5nG08OF+myt1OpVoikLxjzD/J47ym3nEP0uFp5tP0Uu85CvVqjVqnQ7Qqyc3ZItVZjtKWHTDGHWqGk1e1h8/iQoNNNsVLGa3XisNlY3d2jVKnw3ugIDxeXeG/gFga9nrnVLWxmIxaTgbXdEB1BLzalidmFbcaGOlnfPqRYqjB5u5+puXUeDA8xea+XhzMbKBQyRoZamXm8hdGgIeC3o1DIMJvVWCx6NjZOaQnaKJerHIQu6O52s7cdQeUwMtTn5eAoRjZX4tZwgM3tCIVihTujrSytHTPxoBvLaAvza2GqtTr3RoI8WQ1Tq9W5N9rC7PIR9XoDg1zgK+tn1OoN7g74mNs4ldpGO52s7F9QrTcY6/awHrogkSsx3GJn7zxFrlih12clksyRzJVodRoplquEomlcZi0apZw/WAgR6HBhUCtYOIqhkAmM+G1Nec7JTlcTHB50uJjZP6fRgE8PmHn/VGpZDRpVZIplQsk8ZrUct0HTjBYmbkQLP3KnnX/8bQPIxK/PyTYQCLCzs0NLS8uHel5utqde6ya8jWSnTqd7bUfRdY3veQceCATY29sjlUo1011v02YqCAKBQICtra2PCfG+0fajP/qj/OiP/ugf63tqtVru3r3Lo0ePXjl4c11LyGazGAxv151Rr9dJlVJc5C+4LFxykb8gko0QyUUoVAqUa2V2k7vsxHdoM7fxtaOvYVQZsaqtHKQOGHYOsxxdptfWy2ZsE41cQ6VWQWgIDNkHmTl9RKac4TOtf4Lf3f48BqUBAak1tdvayWHyiKCqFZfTztT+Y3QyLX69n5WTdVqMPsLJUwKqIG6vnYXwKhqFGqVKztPDLdocftKFLLFcilttw3x5/gkNGtzrHeHR5hIBmwunyczm8SG9gVYiiRjJbIaR1l6+NP2Uer3Og5FhHi4uoVOrqYk15la38TptiKLI7uEJA12tHJ1GcbbYuTvWw9ySxH8kdSGtNbuQ3v/SFjqtio52N3MLe9htRkwmLWsbx4wOtSOKAgcHF/R0e4hepEkkcgwPBdjdOyefL/Nd7/XwlZkdypUad8fbmFs8pFarP9OuqoTmUNrkWBtTCwcvWbfy5ekdbEE73QEbUyuS03owFGBmVZpqvt3rZmE7Qr3ewGfTU2o0yBUrjLY52DpJUChX6fNbOI3nSeWfBQenSUOXTc+Xd88xqOS02A3MHV4iE+B2q+OZVNLDG11JJ9EUhUqNfoeBcLpAutzAqVWiUcrZvMi8UFv4n7+1n7/zie6va6rD4XCwublJLBbDbre/9e89354Kb07JXHcotba2sry8/MqOouv3v2kKhQK/38/BwQGjo6PNvW9z+rfb7WxtbXF5ednkfPoopo8+8qDw9bLJyUlmZmb483/+z7/09esiWCKReCko/Nryr3GQPCBZTpIsJMlVclwULjjPnlOsFqnWq+QreSr1Ci6di4AxQKlW4un5U/x6P/lKHpVMxZBjiFghxj3vPWTIuO+5T61e447zDqlSCp1Mx3Jimf3YPvlyngFDPzuRHUxyI1pRx/TpDH3mHnaT+1TqFZwOG187eIRDa0Oj1GDVWril17N+tkWpWqa9M8jvPf0aVq0Ju9HG46On3OueYO1oh0wxx2TvbaZ2nqBTa+j2tfJocwmPxQ6iiEatotffwtFFhHyxyOTgKA/X5tGqNPS3tzG9tIzVaMButjCzsszk2G22Q2Eu4jHG+rtY3z2kWC6j0IpMPZEA4cHtPh7OrqFSKujvDvK12WXujA+SShVYXj3E77PSaMDefoTuTi9H4SharQGH3cBxOEY+X+bO7TYWl46oVCSivP2dCOVKjcmJDqZmpe6kmzML793r5Mvvb9JzqwW7Vf8MCDy7DgFwp8vN7zzZl353WJpkBhjrtDO3KTVCXAPF3bG2ZwjybrU72Ay/CA4tDgPlap2Do0tsOhUWrYrVkwQahYxut4nHBxfS3MGNVNLNIvS33mln5iRBsVrHr1dIdNzJMma1HM91tCDAL37PLf7CWOsf8Wl5s4mi2GxP/TCgAB+0p5pMJlKp1Bv3X4OC1Wptcij5/f4X9lxf1/N2PalcKBTQaDQfiktJFEX29/c/FBHgu2Yf7Tjn62if+MQnmJmZee0es9n8yta3ncQO85F5ti63OMmeEMlFkAtyfHofrcZWOi2d3Pbc5pOBTzJoG0Qn6mhUG/SYevCpfRzEDyjWiqTSKTZiGySTSaZOpzhPnjN7Pku2kGU7tQ1IN6NckNFubmcts05DVcesM3NWPGPcN4Zap6ZBgzv+cfazBwTNPuRyBUfJMDqthuWTdSq1Kndbx1gIL+ExOdFr9GxH9rnVOohMJl4BwjhTm3PIBJHxrn7md9doc/moNRocX5zhdljZPQ1LgDB0i6nVRelzh/qYXVvHY7ej1+rYPjqiv70NuVLkIp7k7kg/S1t7Ehvr2BBfm1tkqK+VO6PdTM9tYDRo6Wj18HR1D4/TitGsZnvnlM52D4VChZPTOEODQU7OYsQTWbq7HeztX5LPl3lwv4u5+RCVSo33JruZebTLzuYp3/6JniYgPJiQAEEQBe5PtPNwdg9RFGhzm5laCCGKAvdGgi+sBQHuj7awvXvl+Ac/AITJ4QALu5fN9TUfkqJWY/Xokmqtzt1uN8uhSwrlKrfaHYSiGVL5Er0+K6l8mbNEjmqxQqtNz+5FGotWSdCmZ+k4jvJKx3nmRirpGhDutTupFCsUq3UGnAZS5QbxUg2XXoVZLdUW1HKR3/gz9/67AMK1+Xw+YrHYW80Q3LRrx22322k0Gm+kl7l24tcdRdcF4Of3vCr1q9VqcblczUL122okXNNmZ7NZEonEW/7r3j37GBReYffv32dvb4/z8/NX7rFYLCQSiZeS0vWaehFqAmJVRKyICBWBZCZJJpehkC+QzWSJJWKcx84JXYZYOF9gMbZIuVomX81zWbqkw9BBWSzTZmzDZ/Mx4Zmgz9vHpH+SVmcrI84RlGolCpmCzdwmBrWeMfcYF4ULTGoTk8EHPA7PolOqGXD18SQ8j0apRqfSNesK7x9MY1IbGPEP8Di0gFalxmmycxQ74W7HLZaPN8hVsty/KjRbdSa8VhfleolefzvxbJpoMsb9vlG2oiFq9Tp3+waZWnmKUaenzeOnUCnQ5vVQq9c4ikS41dPD/vEph9ETJscGeby0Tq1W5/7oAA8XVtCqVbhcRp4sbuOwmXBYTaxvH9EWlLp3Vnb3GBwIEokmiMUz3BnrZHPrhFyuxIN7PewfnlOt1rl3t53pmSuOpAddPJzalhz5vU5K+bKksjbWyvTsHgqFjPGRIDNzB6iUckYHA8w92UerVjDa6+XR0hEqpay5VipkjPX7mVk8JHR0ySdHgkyvHiMKcHfAx9QVOAy2GJvr94aDvL94xJDfxmSfl8fbEhHeTXAYbXNweJEmmSs1C9KqegOPUYNBrWArksKgktPtNjN3eHnVlfRsKunRfpTl3XMm/Bb24jky5SpejYxarXZVW1Dw2//DJH+yx/N1fIJeNLVajcPx4eU6QQIGnU6HIAgvZU+9aTcH3LxeL6VSqdmhd3PP607/N3Wc35a64lp0KxAIsL+//xb/qnfTPk4fvcIsFguDg4PMzMzwmc98hmKxiCAIz6hIlUolyuUyT548oVarNZWlABR1BYlMAgSoUQMBRJlIvpLHpDFhUppQikoEmUC1XsVWs6GUKVHL1BxnjrGqrbiNbqZOpnDpXKzEVojmo3Rbu9mObxMwBjhOS87GorLgVDixKC186ejLCAj4fR5+Z+vzmNUmakKNpbMVBl39hGJHDDtHmvMKRpWBIXcfX92eocfVyXn6Ar8zwGTXbaZ25lDI5KjUSha31/GYHSjkCrbPDrB2mjm6OCNfKvBe/xgP1xdQyOTc6ujl8cYqDrMFg1bHxuE+ox09pHM5Yqk0dwcHmVvfoFar43PZCR9eoJDLGe3tZGZxDbNBj9tmY2F7k4DPQa1aZ+/wjL6uIKfnMVLpHOPDXZQSDbLZIg/u9jAzuy3RVtzv4+HMBgB3J3p59FhSVrtzu52p6R2UShnDQ0FmHu3S2e1isM/H7EIIvU5FW6uduaUjjHo1AZ+FheUjjAY14yNB3l8IYdSr8LvMLKyfYNSpCHgtzK+F0WkUdATt1MtV1EoZfa0OHq+doJCLjHa5ebJxKqV5Bv3NGoVZIfL7G1InzmSfl6mr9d1uN/N7UlppuNXOXkQqSCcv08g0Ko7iOex6NSaNgtWTBGq5SJ/XwqN9qYVy8kYqacBjpl6rU6zW6XcaOE7mJXAwqPnffmiSAeer+/e/nhYIBF6Z53+dXasMymQyDg8PXzshfRMUZDIZgUCAUCiEzWZr7nnT6d9sNmM0Gjk6OnqhzfRVdh2htLS08LWvfY1sNvtWdBvvmn0MCjcsHo/zkz/5k5yfn3N+fk44HOazn/0s2WyWH/uxH+O7v/u7X6CwUKvVzXDzZmuqKIp88b99kXhROqGUqiVq1MiWs1zmLwnnwlRqFfKVPA0aeA1evHovsUKMtcs12s3tZCtZdHIdfdY+ovkovdZeatTw6ryU6iXaTG2c586xaqzMnMxQvCzh0Drw6D2sxdbwGjwoZApmjh/xqbZv5dHhE0rVEgaNjt9f+wo2nRWzxkSlUWbY18/uxQH5UgGNSsUXlqbQKjV0ulp5vLfAt3R/gvXjXc4uT5noHGb+YIV2ezt2k5WH6wvoVBraPQHEmojLbEEml7N/Gmaks5ut40M6HG30tEh1BYD7w0NMLS3zycHbmAw6nqxu4rJb0CjUbO4f0dnixyAYeLq6z+hAO1t7YQrFMvfG+5h9usW9wYFnQODBvR4ezmwgk4mM3+qgUQOlUmSgP8Dj2T0MBjUtLXbm5g8wm7TIBZFctoTNqsNi0bGycXo1xKZmbesMp92ATquiUijjtOrRaZWs751jt+gwGdSs7USwmrTYLTqWt85oD5Zp91p5uh1Bp1bQ4bPyZOMUpVykxaFhZjWMKMBEv5/fn9rG1e6k02tpAsJNcJjodPH04IJKrc5AwMbxZYbefhOiANV6g72LDGatEo9Jy9OjGDIBxlsdTfK868LzUJudca+ZtWhaqi1oRP7ff3rsGwYIIB22lEol0WgUj8fTVFu7PmBdH7iel/G85hC7bgVPpVIvJb27Jpy86fCDwSBf/epXn2EzfZvTf2trK+vr68DbtZleg4Jarcbr9XJwcPAxKHzU7XqW4NatW7hcLtbX15mamuJXfuVX8Pl8KJXKF35HJpNRLBZfUGACcOgcnOfPqdQqVBtVipUiKrmKgCFAtVGVSPFEJSqZCoVMQa1Ro1wrM+QYwq61s3i+SKlWolArsB5bZ9I/yVR4ignPBLNns9z33WcrvsU97z2cGicuhYuyWJE6lKw9qJGxdbnNveBdaciuXmPi/8fef0dHnt7nveCncs45oQo55wYaDaAnkBRpKlhOR7Kv15K8pMLlWfEqWMeSeI/OWa+9Wvl4ubo2JXK9K69W1zparSSvrn1MMU9CaOScYwEoVCEUKue0f1QD7J7OzSFnhppn/ugfCm8FDH54n/ebnsfTz3f23qTO5CNfyrN3eYDNZ2MztEO+VGS4bpBvbr6Fz+xDJpGxfLxBi6OeiqDEeSzMcFMfkzsLCBBQ53LzN9NjGNVazDojK4fb9Ne2k87lSEQjDLa0s7C7RaFYxOO08DdvTVejgqZGJpdXMGo1ICqxvLWP12kjly1yGAjR0VTL4UkIW72Zwd5m5ld2KRZLjAy0MT5T/SOVqYS88fXvksDEvS0UCinNjU6mZ3dorHdit2tYWPRjMqkxGFSsrp5gs+lQKCRsbgV5/VOdZIsldg8u8LgMlEpl9g4v8bqN5AslDo4ukciEyGUSDk6u8Nj1lMsV9o7COK3V+YLtwwtsJjWVcqWqiqpVYNYpWd47Q6uU4rHpWTs4RyoW0lFv495alRx6a0x8baWaRnmQEIZbqqJ4lQr011tZPQqTK5SQFookc0WuUjlsWjlyiZiNYBSlRESjXcf0wf1o4YFOJLVAwGkqR7ZYZsBl4P/cb0KYvAJefOL/RVCpVB67qV//W6lUWF9fZ2tr67uR9bvUf2UyGWq1+qGD1rUC8MHBAX6//4mkAA9v4nK5HLvdjt/vp62tDXj+2YPNzU3g+QbmHnxNn8/HxMQEmUzmiaoIH1QIKi/r/P63AMfHx9TW1nJ6eoparX7smnA4zPr6Onfv3n3ke3+58Zf8xfpfUKqUKFEiW8ySyCeQiWWIBWIqVP/XCxCQLWbZj+5zlb2i09qJRCBh/myeTksnmVKGcrlMvb6eeD6OSW4ilo+hlqo5TZySL+XZutoCYNg+ggAh04EZbtkGEAlEjB1N0Gvto1yEpdMV6oy1WORWpg7nuOMbYMo/R722EYNCz/TBAjatlWZTI29vTtPtaWP7bB+VREWzuYnxzTmkYgkdNdWUUDKWRyaR4D8/paOmkcPQKbKCkjqnm9mdDSqVCsPt3RwGg8TO89R73Czv7GI3m6rPOw0x2NDDzkGASDxBf0cTq9sH5PIFXhvo5a03N6s1gfuEIBIJudXVyNTCFl01zQiFQhaXD6seCg4Dm1sBLGYtGo2CUkZMNldAIpFycnKFz2smmy0QOotRX29FKpeycRqhqd7KZTjJVTRNc4ON84sEkViapnorF5dJ6jvcxNK5G2vO+hoT8WSWi6sUXqeBXL5I6DLBK8NNHISTHJ/HMesV6FRy9gIRNAoJZq2Ug7MUcqmINp+VcDLLcaHIYJODe1vVHPloq5Ox++Rwp9nB1HaIcqVCt8/CbiiK1mVELhGTLhQ5i2cwKqVYNAq2zmJVxdUaM9OHVXK4jhZGumpQa+T8r/9okEI6ycLCAq+88soLD1hVKpWnnujffbqHqsTFg0OcD/ozb29v097efhM5PG9vf6FQIJ1OMzMzw6uvvnqjnnqNYrHIt771LT7+8Y8/5JUci8WYnp7mtddeQyKREAqFODg44M6dO099v93dXXZ3d/nUpz71zPbSw8NDIpEIvb29ACwsLGA2m2loaHiun+2Dgo8ihafA4/HgcrmYmZnh9ddff+wavV5PLpe7aV97EIPOQf7z6n+mWCmSL1VPSEKBkEg6glamRSVVIRFWb1yRQESrqRWZuBo1+GN+LAoLOpmOlZMVanW13Du9RzKfxKl2EkgG0Mv0RHNRAFqMLQgLQiqlMhOn95AKpWgVGr6+/S2MCgNF8myfH9JmbeEkFsCmtDFSO8T4wT3kYhl15hq+vvoWXqObXDFPtphloLabxaO1qhKqt4OLyys0chVei4v5/VV8Zhd6tYbN433669tZPdwlV8jT19DO2ytVX4XexhYm1pYwarR0NDYytbJGrdNBOluV1O5qakAqFhOJJxjqaWN6eZNyucxofydvzizQUt+AXqdmfGYduUxCa2MNUwtb6LUqbE4d3/zGCjarDoVCxuZWgBq3mUKxxP7BGaO321hZDnF2lqTlvp9CNJqmo92F/yhMIpHlYz/Wy9TiIal0nq52F7v7VeOdB681UjEbBxekMvkbr+ZEKkdLnYXQZZJoPEN9jYlD/wXnhTIeq5ZSucJeIIJVr0SpkHAQjKFRSnFbdcxvB5FJRNy908hb6wEEwJ0Wxw0hPEgOD7avDls1TAcixDIFnHolIqGArbMYKqmIeqvuhhAerC20aBX8X3/qNhKRkIpEh0wmu0ndXG/0T0vZPPg48Fi5FqVSiV6vf4gAZDLZUzf66w6daz2j58WT1FOvcT1/8G7S0+l0aLVaTk5OqK2tfe6OIrPZzO7uLldXVw/VJB6Hd79mZ2fnI3vChwEfkcIzMDo6yuTk5BNJQSQSodVqiUajj9wANboazEozsWwMmUhGvphHIpQgQMBF5oLD2GE1PVTMIBFKcKqd2NQ2gskgm+FNWk2tXGWvkIlk+HQ+5GI5VpWVfClPk6mJXDGHTCzDH/NjVpoZOxlDnBDTZmkjV8zx9tHb1BlqKZQKrJyv8iN1n+Sd/QmyxRwKmYzvbIyjlWtx6ZwEEqc02eq5SFwSScdotNYytbVS7Saq72N8Z5ZX60colyusHm/T4qwjFLukzepiqLmH6a0VyuUyI229hGNRZGIJLd5aZjbXsBvNyMRSJFIhLT4fwctLYskkA+2tLG7t0Oz2MdLfwfhcVV57uLedsbkVpBIxXq+Fr397Aa1GictuZmF1D5tFj0IuY21vD2+NmXy+xKH/nKYGJ5fhOFeRJB2tNZydx4jFsnR2utndPSeTydPf52N17YRcrsjArTry2TypdJ7BXh8Lq1XjnQevB3q8zMzsI9Ap6G93s7oTIpcv0tPqZOvggky2QEeDHX+wShQf/3g7C7vnXMUzeO068oUSh8EYRo0UpVzKxuEFWpUMt1VLIZO/kc2e2KxGCyMt3yWE4RYnE/ed2frqrewchYnlS9RbNMQzBU6TWYxKGWaNjOWTK8RCAb015pvawi+N1vPrr3o5PTm+2dgrlQobGxtsb2/fSL6LRKKHNnmZTHaz0T/4uFQqd4/zlwAArfZJREFUfc8kHDweD9PT0zQ2Nj50on8Wrjddh8PB1tbWjXrqNa7bVR93qvd6vWxubuL1ep+7o0ggENykrJ5FCu9+zafJ43+Q8REpPAOjo6P85V/+5VPXXA+xPe7UY1VaOU+fUyxXc/rpQhqFRIFL5aKkLCEQ3q8riGVIhBKK5SK5Yo4+Wx8GuYHZ0CwigYh4Ps5GeAOTwsRkYJI7rjtMBiYZcY+wH91HLVHTqGtEXJQgF8tYv1in29aFqCxlPrjAkPs2mVKGfKnAkHeQ7+y9Rbezh0Q2xUZoiy5ne1U6Ox1jtGGQd3an6HX1IEDI1N48ToOdXDnLbuiQbm8r28EDMvksapWCb0zdQygQcru5i/H1BcwaPS6TmaW9bXx2J5lsHv9ZEI/FgT8UJJPNMdzVyeTKKpVKBb1eyeryYTWyaGtkYmENjUpBjdPOpv8Aq1mPSilnY+cIr9tKLl/g8PiM5no3sqKS5ZUjujq87B2ESKVy9PfWs7p2RC5X5PZgE7Nzgao8xVAD09N7VW+FO41M3tvFbNU8NMn8pOu/82oL37i3S7lc4XZXzY38xYNE0dXsIBXLcBXP0FJjInSVIprM4rXrSGfznFwkseqV1aL1wQXOZJZWn4XZ3bMbw51re84Ho4WhZgfTu2eUKxXu9vtYOI2SzJewqaUIqLB9FkcuEuDUSJi5Hy18pkvP3/cIODk5eUiXy+VysbOzQ3t7O1qt9j3d6F8EGo0GrVZLMBh8YetcoVCIwWBALBYTCoVwOp0337vuPHrcZmyz2dja2uL8/PyFZg+kUilXV1ckEomnqhf8MFhxwkek8EyMjo7yG7/xGxSLxSf6JRgMBra3tx/7vR57D3tXe5QEJcqiMmKhmHgujkQkQSKSUKFCsVKkWCiSKWTYvtomVUjRa+vlInNBLBej19bLafIUr8aLRCRh0DGIXqZn1D2KQqygw9JBMBUknkmQK+UYVNxmxDPCxPEEd5zDjHpGGPNPUKv30ePs4p5/Go/OhUGlZymwxq2aXpYDa/RYu6m3+hjbnUYjU2PRGfnG8jvUWmpI5VLc25/jldYRJrcXKJSKjLT088bGBEaNAa/VydTWMja9CYVMjhI5dTYXV4kE0WSCwdZ27m0sY1ZZ6W9pZmxxGYFAwFBnB2OLy4y23iKRyDCzsonJoMOgUbO2c0CNw4rDZmJp7YDmejfnl1EisSTdbXXsHATobTIx0NfA4soBhUKJocEmpmeqm/fIUDOFHJRKZUaGmxifqP6ORkeaGBuvXjc32InGM484sY0O1jM2/d3rYCBSfc0HJpnv9HiZuq+BNNjpYWHjlDIVhm43srR3TiZXoMVrJhROEk1mseqkCIQCDk6jmPUK5DIJokoFhVREnVVz48DW6dHdEEKnS829nepwXKNFzlW4SggenYxErkQ0W0SvEGNUytgPpxALBXzlfzfCP7n95Dx2LBYjkUi8lMT8ewm3283+/v4jUtXPwrXr4bV66rtJ4Ukbs0AgoKamhsPDw4cE7J6G69kDs9nM4eEhnZ2dT1xbLpdfKOr5oOKj4bVnoL29HbFYzPLy8hPX6PV60un0YxUZBxwD5Mo5suUsyUKSfCmPUCgknA6TyCYQIUImkiEXyVFJVPTYevi47+NYVVYKpQIejQe1VE0wGUQpVTJ+Ms7S+RKTgUnGTsZ46/gtdq52uEhf0GvvpVvfTSwXZfx4HKVEiVQiZcw/gV6uQyaWcZ68oMFcT7qQ4Sp7xR3fAPPHSxTLRYwaPeO705hURmxaC1sXO7Q6G7lKRjiPhxlu7K8SWKl0M8ymkMrorGtiYW8Dr8WJUCDk8CyAXqciEL4gmkww3NHNzOY6xVKR3rYGxhaXkUrE9LU0c29lFYNGjUwhZGlzD5fNjFwqYfcoQJPPTTKdQaOV091Wx/HpBZFYksGeJta3/aQzOSQKmFvco5AvMXKnlXtTO5TLFUaHWxi/t8XJ6TntbZYbQhi+P8QGMHyneq2VSxgeqLshhOGBuhtCGLlPDsvLR7w2UHdDCKN9tUwuVs18hnt9zKyeUCiW6G91QblMJlegw2fiMBghmszis2tI58qcXaWw6qRUKmX2TyMkw1eYVWLWTqJIRAJanFqWj6tSDgMNFlaCKQCGmuzsXmbZDSS45TUTyVYJwaVXopZXCUElFfNXn/vEUwkBqgNdp6enz/T8+H7DZrNRKBQeGSx7Fh5UT00mkw+pCjwrAnC73SQSCVKp1At1FPl8PoLB4BNVV6/XvptoPkof/RBCKBQyPDzMxMQEfX19j10jkUhQq9VEo9FHTl8+nQ+TwkQ8F0cukpMv5ZFVZAgRcpG+IJAKkCvmyJayKMQKnBonZoWZUCrEbmSXTmsnwWQ132xT2ciVcni1XtLFNGqJ+uZ5O1c7iIQilqJLAIx47uKP+Xnz8A267X1cZSJsXm7xydpPMnEwRTKfotXawsLBGhKhhHZnC9Mns7gN1VPX7sUB3e524vEssUyC0aZBxran6XN30V/fweT2AmatAZ1CQ66Uocnl4yJ2RSQZZ7Cpk7XALoVikTvtXUysLiESCrnV0sHJVQiNUkmNw87cxiY2kxG5VMY7Kwu0N9RxFo5yGYnR2VzH/tEpqUwWkazC+rafQrHE8K1WJuc2qZQrjA628+bEMo11PqxmA+MT1fbB4dvNjE1sIhQK8NSYOTtN3ZjtTEzsIBYL6e3xMTG5g0QiQlguMzl/WH28s4aJmX1EIgG3ur2MT+8hEMBATw2ZVBaAW20Oxu5rIPU0VT2cAdrq9EyvHONxaWj1aFg/uqJcrtDi1nF4niSbL+EyyUkVIJrM4TSpyecFpBHcN9nRsH4cRiQU0N9oZ/p+hPBgKqnLa0YigGSuSINVSySVI5zKYVbL+C+f+xH6vc/WFbrWHrq8vHxsK/UPCkKhEJfLxcnJyTPz9Y977rV66oPtqc+y67wWvLu8vHyu97yOPNRq9Y0yclNT02PX/jD4M8NHkcJz4Xl0kK4lL94NgUCAVWUlV86RLqbJFrPEc3HEQjF2lZ06Qx1tljbuuO4w5ByiXl+PWqLGpDAx5BzCrrQTy8UwK8yEM2H2o/vky3mmTqfIlrKMn4yTKWbwx/0Ek6d0mDtoUDZQqZQ4iZ/Q5+xFI1dxHDtm0D3AVfaKZD7FiG+IscMJulxtNFjrmD9eQq/QYVYbOImcMljby9rpFk6DhZHGAca2p1FJlSCCFf8WbqMdmVjK3tkRZQoEry6IJOMMt/Uys7NKJBXnVlMLk2vLyKVSuuqbmNpY4Sx2ic/pYG1vH5/DARXwB4M0ejyoVAouIzEGOprZ2j8ilcky3NvOW7NLWC16RgfbmZjdoFKuMHKrnbGpqn9zQ6ON8clNJBIRA/31TExtIZOJ6enyMTWzg82mptZnZHpmH5VKSluri5nZfZRKKU1NdsbGtulotNLgMzGzcIhUIqS+xsDU/CFikYB6r57peT/B4zPaag3MrldJurfFxuJ2NYd/u8vN+n4UALfFSDInqNYf2lzsBhNk8yW6GmxcJgtEkznqnQYKpTKHwRhdbsN9k50wSqmYDp/5hhCGH+hKGm5xMrt3xtVlgk63gWAsTTiVw2tS861f+9HnIoTre/I6Wni/4Xa7ubi4IJvNvtDzrusGTqeTs7Ozm+c/T63A6/WSSqWeqaF0/XoP+jgfHx8/4on+uLUfZnxECs+Ba1J4Wrj9JFIA6LH1IBfKUYlVaGQadHIdxXKRChWkQilioZhypUyqmOIkccJbx28xF5yjVClxnDjmIn1Bnb6O3atdnCon5UqZHmsPSrGSUfcocpGcTksn5+lzztPn7KZ3SeVTDHvuMB9cIFNKM+odZvpkhs3LDe54Bxk/vIdJaUQlV7IW3KDN3sxlKoxaoWS4foDpgwXKlTJqhZLxnRmMSh0ug4P5gxWGW/rIFHIErs4YqOtk0b+J22xjtL2PifWFqndzcxclQRGVTE6d083CziYusxWpWIJSKaPF5yWaTHJ2dUV/Swu7x8cgKXGnt53ZtW3yhSKj/Z1MLKwBFbo6vIxNryESCRnsbWZ8purf3NNez+ruASqljJYmFzNz96eXa8zMLx6g1ShIZ9Ps7oXRaGQYDQqWV47RqKUYjHLWNk7RqGXIRBU2dy/QqGR4XAa2D65Qq6Q01lvZPYyikEswaLTE02UkYiG3OjwsbJ7diOJNLd8fROuvZXLpCK9Zw0inh6n1AMVSmcE2FxtHl+QKZRqcWs6jKS6iabx2HclohoOzGEa1DI9Vy9LhJRKRgIEG201X0mhrtROpUgGNREQmVySVK9LhMvDtX/9RGm0vZnXpdDq5uLh4YTe09xoKhQKz2fxSekjX7akGg+HGa+F5uoqUSiVyuZxkMvnM93hwozcajSgUiieS6Uek8LcIt27dIhKJPFXkSq/Xk0wmbyY0H3q+41a1rlCqDq9lC1nKlTLhTJhwOlwNeQVCxAIxaqmafns/H/N9DLPCjFQopc3UhlwiJ1PKYFFZuBe4x2HskLeP32b6dJpv+79NIBkgWUjSammh11gtTM+dzqORapCIJdw7nkYjVVNnqiNTyODRuZBL5Kycr9Ln7mL/8pB4NoFCJmNibwaZWEqPp4Pv7LxDrdmDRq5hO7hPh7uZEkXCiQh3GvuY3VsjXyxQ63QytjaPXCKjs7aJ6a1l4oUkWoWS9cN96p1ucoU8JxdnqNRS/KEQ0USCoc4OFne2yRUKKJRiZle2qp0/fR2Mza0gFom41dHE3skxcpmE5lo30/PbqJQyXPaqf3M0Ecfj1rKydoROJ0etkrK9E8JkVKFSSVlZP6G9zYpKKeX4JIbDoUNv1BA4TeB06KuGPCshPE49JqOavcMwZqMam0XHxvYZBp2SGreRpbUT6hw6WuqszK4eI5N+VxRPKBQw1OO9qTlIKd/4K4x0eZjZOqVQLNPTYMV/liCRztPiNRNL5phZO+FWvRW1SsbWaQS1XEyL28TM7ll1hqH5wWjBwezeGTaFlLuNNr7xq5/GoVO+8D193XL6QYkWAoHAc53cH8R1ROByuTg+PqZcLj8zfXQNpVJJPB5/4qn/Go/zcX6c6ur12h8GUviopvAckMvlDAwMMDExQX19/WPXXPd2R6PRR/K0dfo6jHIjqUIKuUhebU+tlJCJZQSTQbYj22SLWfKlPBqpBqe6mtf3x/0cx4/ps/exH6kSklqixqK00GZuu0krZYoZNBING1cbpIsZFq4WAPhEzY+wdrHOvcA9Rj13CcSDLIdW+JjvYxxHA4TTV9yuGSAcjZEt5hiuvc03t9/AY6xFK1cxf7SMz+TBprBwb2eBPl8naydb6BVXjDbdYmxzDpFQxK2GDjZOd9Cp1DiNVhb3NvBY7KTyaUQiCc1uL8GrS+LpFIOt7cxur1IuCbjd0c69lepsQn9zE2/NL9BaU48AIRPzq0glYtxWI7Or26gVMrxOJ+vbxxj0KtRKOftH59jMOsRiMQazFk+6TLFYJhiKUOu1ks7kCYai1NXa0BmUrK2fU1dnJZHMEjy7otZnIZXKcRqM4vOacTj0TM4d4nEZKJcq7B1eYLdqkUnFbO2eYTKqKKTyrOyEqqJ4Dj1zayfIpCLaGx3cWzpCKBQw2OnhOxO7tHTVYDaoGLtPDnc63EytByiXK3T4TOwFo2RyReqdBjRSMbMXCUwaBQa1jBX/ZXWGwWth8jETzx61nD/4hdeRS17+T9jlcnFwcPDCbmjvNUwmEyKRiPPzc+x2+ws999rX5Lo99d0Wm0+CWCxGIpFwenr61JbYd0cedrud7e1tzs/PH6kfflRT+FuGa9Odp+FZdYVsKUuqkCJVSBHJViW37So7NZoaWowtDDoH6bf1U6OtQSlRUqOp4RXPK1gUFiRCCY2GRi4zl5ynz8mX8iycLZAuphk7GSOSj3AYO2Q/ske3pZs6RR2pQopgMkivvReRSMRB5JBeRw8n8WPC6StGfENMHc1g11kZ9PYzcTCFSW2kzuJh7XSLFnsD0UwcgQiGGnpZOlonV8zT4PASjF4gl8jo8jYztbNEMp/CZ3OxcbxPrc1NIp3iNHyO02LiIBQgnk7RUVPLzMY68UyKjloPU6trCAUC2n1e5ra2kUkkWCxa1veP0apV+Fx29gPn2Ex6zEYDZosej8uCQi7j+DRMnddOuQKBUJiisEAqlSMYitDa4uIqmuTsPEp7q5vLyzi7+0G8Xj0X4QQXlwnaWp2Ew0nOL+K0tjiJRNOUsgUa66yk03kCoSi1NSbK5Qr+kyvcDj1ymYTJ6T362pxYjGrWds/QqmXUey3MrwcektYWCKDWqrkhhNFOD5OrJ5TLFbrrTGwcXZHJFemotXAeTbG8doLXokEuFbEbjKJVSGh0GpjdezRa+OwnOviP/+PHvydCgKq2Ty6Xey7jmu8nBALBjQHPi+K6tuByufD7/c99Wi+XyzeF46elhd/9ek/ycX7c2g8rPiKF58T3UmwG6LZ2oxApUElVaGVazEozgvv/KaVKFBIFAgSkiin8cT9v+N9gLjRHrpRjN7LLQewAk8LE9tU2RrmRWC5Gk7EJqVDKsGsYuUhOj7WHfDlPrpxjP7PPRfKcYfcwC8FF/DE/I947LIWW2Q7v8HrDK4wf3kMhViCXSpn2z+HSOe6nqVJ0e9rxhwNE0zFEQpjaW6RSKdPjbmN8exa9XIlDa2bhYB2r2kCpWKKQy1FrdhKKXBBNJej0NHCeDJMvFhloamP16AAEcLu1A4lKhlwqpbupkbVDP3q1mlqXk7XjAxwWIwadmu3DE7xOGwKBkMNAiIq4SDqd5TR0RXtzDZfhOBfhGF1ttaxtH6LTKenpruXw8IJYLE1fTx17+2fEExk8HiMSqYhEIktfr5f9gwviiQw93d6b9cV0nkg0TTiSoq3JzlUkxfllgoZaC5lcgUAwSo3LgF4hZe84jNWoxmRQs35NDjVm5tcDSCUi+tvcTM7sIxEJGe703JDDSKeHpf0wpXKFviY7OydXJNJ5TBoFNq2CQDiJRafAolOydhRGKhbSV2+9iRa+8I8G+f3PvIboPfABFolE2O32D0QKyeVyEY/HnyvP/yCu21NtNhvJZPK5W03L5TIGg4FCocDl5eUT1z2ucH3d1vpug62PSOFvGYaHh9nZ2eH8/PyJa/R6PYlE4rF5ylvOW2RLWTLFDPF8nES+Omh2lj7jMn1JIlf9ulQpIRfLueW4xas1r2KUGzEpTdx23EYhVqCT6aoOa5drJPNJ3jx6k7XLNd48epNYLkYin8CusdFv6iOUCXEQPUQpVmLVWNi53EMsENPv6iOdT6OX63Bq7Lyx9xYNhjpSuTSB6CmpdJKN020yhQztpkbGDqao0TtoNNeyeLKOQalHIBVwEA5QZ/VQqJS4Ssew2k0Eohdk8jlG2vpYOd7l8CpAl7eOme11pGIJfU1Vv4VA5Ix6j5uFrW1sJiN6rYbNQz8alQKnzYQ/cEZLrYd4Mk3o8orOpjpW9nYB6OuqZ+8wSDyZZqCnkY2dI9KZHM2tdlZW/VWJ7cEmllYOyeYKDA02sbB0gN6gpL3NytLyMdlsgduDdayuHZPJFhi4VcvK2gl1NSb6umrY918SS2TpbHUSOo8TvkrRVG8lmcqxtnKMz2VAJBZycHKF1ajGrFexvnuGRiWlyWdhdu2EZDLHa901TDxQW7iuM3R4dSzunJErlOiqtxG4iEO2gNeiQSwUsheKVaMFh4G5vXOEAgH//rOv89v/6PZ7mpZwuVyEQqFn5ta/35BIJNjt9peOFq7bU6+urp57/kAsFt8Msz1t3bs3eolEgsfjeSRa+IgU3ie8/fbb/MRP/MSNycZf//VfP/M5b731Fv39/cjlcurq6vjKV77ywu9rNBppa2vj3r17T1yjUCiQyWSPDccbDY0YZIabjV0n1WFUGPFoPEiFUgLJAOuX6yyeLXIUOyJdSJMsJJk/m2f6dJoKFVYuVojmokhFUoQIadA30GBoYMAxwB3nHRr1jdTr6jmNBZkLz5MsJqlV1KAWq5gOzGCXWLHJrMydzpNIRpEKpOxFDvDpvCgkMqLZGLec3axfbdNgreV2bR9r4R00MjVNnjq2LvbxGJ0oZDJmj5e53djDWSxMJBVnqKmHie05ZBIJI+19jK/PIxKKGGzuRCAWoJTJaPLUMLe1gVVvQCwWAhW8DjsCBByeBmnx+Ygmk8iVErpb6jkKXRCJJ6otqgdHJFIZBm41srR2QDZXYHigldmlXQqFEiODbWwdHlWnl++0cG96+6HrcrmCUilmY+P8/uONTE3vUyyWGR5quLHs1MrFLK2dkM0VGejxsrV7RjKVo7vdzclplKtoGoNWgVGnJHiRwOvUIxIJ2D+5wmxQYTVpWN0JoVJIaGuwEY2kqu5oD7ixjXZ5WPXHKFcqDLY62fBfkMoWSMXTVCoQjKSw6BSYtUrWjsPIJCL+9Fc/zWc+0fHC9+2zoNFoUCgUT3UY/EHB7XYTDAZfmKAebE9NJBLP9ZzrWoHH4yESiTzxeU/qZvJ6vZyfn5NOpwFubEI/qim8D0ilUnR3d/OlL33pudYfHBzwoz/6o9y9e5eFhQV++7d/m89//vP81V/91Qu/98jICBMTE09d87S6gkVlIVfMkcqnSOQTXKQvyJVyaGQaarQ11Onr6LZ2025px66yIxfKqdXW8orjFVRCFWaZmU59J6FoiDJlLmIX7ER2CFwEmDydZP9in73YHruxHVq1rdQr6oiV4pxnL2g1tqDWKjnOnNBibiYiiBPNx7jl7uM4EUClVjBaN8Ts6RJioZgas5Opg/mb6ebj2AkNdh/pfJrTyBm3ajsRCCGVSzPS0s+97UUKxQLD7b2Mr82jkMro8DUyvbVCRVzGqNayerBHjdVerW8EA9itBmLJFKFwmJ6mJvyhINFEAqGkzPqun3Qm+1CL6khfB6GrS0qlMqODbUzMVKW5RwfbGJ9e5+A4yMde72B8sjrENnKn5aHrt8fX8fkM3OqrYXxyB4DR4SYm7u3et+xs4u03N1AqJAzfqmN26Yj8fYG89e0g6Uyeng4P/tMIMoGAlloL8WSO4EUCj12PVCJi7yiMUafEZdWxvBVkezvIrRYn99YCAAx3um98nNvcaqY3rruSbOyfRnHrlTfRwv5ZDJ1Syv/2Wz/J3x18fIPD94rrfPwHIYWk0+lQqVTPtNt8HK7bUxUKxc1G/TRcp4VkMtnNANyT1j2OFBQKxSM+ztef48OOD1330ac//Wk+/elPP/f6r3zlK9TU1PD7v//7ALS2tjI7O8u/+3f/jn/4D//hC733K6+8cvM6T4Jer3/iTd1p6eQgcoAIERIkSEVSsvlqe6qwLERUFpHNZUmWkyQKCQK5ADKBjHp1PWf5My5yF/Qae9lP7WOWmQnlQxikBpQqJX2aPtQSNWaDmZ2rHVQqFRvBDYxlI6M1I4wfTaCWqrntHmQxuESulONTDX+Hb2x9h0qlglwq483NSVRSJXVmH1vhXdwGB5VKdbq509VKMpEmnIxyp6GPqb1F+jxdjLT0M745h0QkptvXSiQTRa/SYDdaWNrfxGmyEs8luIzHaXB5uIrHuErE6a5vwn8RIJpIMNjexvzmFsVSieGuLsaWlqlz+nBYjIzdV04d6e9kfG4FsUjM3aEe3rm3VtVO6m9mbLo6xDbY20y+mK9acPY3MD5ZnWoevNXI+OQmAgF4vQbeeLPayTU81MjYffmLB7WRPn6rjr95s+roNjJYz/h9yYvBvlrmV48oFssUM3lOLxLEk1mafBYuI0muYhlcNi1CgYBt/yU6tbxqxgOIRQJ6mxxM3DfWGe3y3JDD7TYXc1tBiqUygmyBWDpPNJXDblDx17/5d+l8zqG0l4XdbmdnZ+chZ7L3C9fWmW63+4X1kKDaahqJRJ7Zmvrgqd7n8zE5OUlTU9MjRlpPG4arra1lenqahoaGx5r7fFjxoSOFF8Xk5CSf/OQnH3rsU5/6FH/0R39EoVB4IQGr0dFRfu7nfu6hP55KpUKxWLzRnS8Wi8RiMba2th56PJ/PU4qXCF2GqiJ4FEEAFUGFRCGBUCBEJpFRokRFWEEil9Cl68KqsiISiNDldbQL2xELxTRUGnCoHYyfjFOrr2XufA6nxslpojrRHM6EaTW2ccvSz050l2g2ilgoptPWQSyVJFfKMeK9QzKfQCwQ0+Pu5M39d+hx95LOpVk5XafO5EMpVbJ9tke/t5vVwAY9th58Zjdj2zMIECCXS5laXapacdprmN1bodbqwaQ1sHm8T73DQ/x+F9Lt2m5W/Iekc1kGW9tZ2Kk6sn1iaJRv3ZuBCoz2djO2UNWYaq538dU3ZhAIBNzubr1PCCL62hrJ5wpIJWK62mqZnN1EJpXQ3uzl3twmTT4P3Z3VSWaZTEx7q4d709tIpWI622tYXjtCIhbS1VXDxL2d+6RR911tpDuNBE+qWjwPCuSNDNYzPlslk9u9PuZWjugeaKBYrrBzdEE6U6Chxkw0keEyksJm1qCQidnYO6dbIaXNZ6n6NQtgqO270UKnV8fUejWK6Gm0M7cRwFJrwaJV8L/91k/i/QFYZ0qlUiwWC6enp4/4E/ygYbPZ2N7eJhqNvrCVpVAovHFne7d66rvx4Gav0WjQ6/UcHx8/0nL+tDrBtUfD8fExDocDgUDwEJF9WNNHP/SkEAqFHuknttlsFItFLi8vn2ny4ff7mZqaIhQKEQqF0Ol0/OiP/ijxeJzf/u3fxmAw3PRGX0sUA2QymRt54OvH+yX9fPub3yZX+q6oVkVQoVQukcgluMxccpG9oFAuoJPr0Av1pAop1i/XiWQjDDmHbgrMJoWJcqWMTWkjnA7TamrFpXJhVVoRCoUcxf0cxaobz4DaRiqfZuJ4kruuV+hz9jLun6TJ0EiztZGZ43lcWgdGlY7FkxU6HK34r47ptHRiVN1i+mC+2q2h0fK1hbeRiiR01rQwtj3NUMMgV/EoK/4tvBYn2UIWk0xLu7eB44sg8XSKgcYO8rki6VyW4Y5uJteWq2mfzl4y+SwgYLi7k7GF5apGUlsLWyd+pBIxnU113FtcRymX0ej1ML28ya3WNprqXcwu7aDVKHE7zcyv7KLVKBFKKoQvEmg1Ctwu081Us8djZm5hH5VSRkeHm7n5Q+RyCa0tTu5N7z2khySWiLj7ejvvTFUL2yO3GxifuU8OA/U31yallDeWjigUS3Q22Tk4uSKZzlPrMpDOFjgMRDDpFaQTWZLZIjKJiI46K5Nr96efO79beL7d5mJ285RSucJwrZXf+/mPYdH+4AxaXC4Xq6urj/gT/KAhEolwOp0cHx8/QgrvPoC92wwol8uRSCTQ6XSPqKe+G+/O//t8PtbW1qitrX3En+Fpp//a2lrW1tYwm81PlOz+sOGHnhTgUca+DvWe5xc4NTXFF7/4Rex2OzabDbfbTW1tLa+//jpDQ0OYTKYbTfrr11teXkatVlNXV/fI69k1dravtimUCpTKJTLFDDKxDKFAiFamrbamVgSopeqqMU85T4OhAa1Ui0wso8PSgVwkJ5qLYlfZyZVyRHNR4rk4M6EZmo3NN9acg87bxGJx9iP7HEQPaTA0UCDP/OkCLo2TbClHKp+jwVxPJB3hLHVOv6eH1eA6uUIejULJ11feRigQMlR3i/G9KfQqLW6Dg7mDFZx6GyqFnHtbhzQ5a6uCeKkYnR1tvL04R7aQ505rD/c2l1BJFbR7fEysVgX7hju6GVtZoNnlY6CtlYmlFRQyGc0+L1Or62iUCnrbmpla2sCgVWM1GVna3MNk0JHKp/D7o1hMOjRqBetbRzeeC5s7J7w20Id/X8j65glmkxadTsna+jFGoxqzUYNQJECtkuLxmFlY9KNSSamvszEzu49UKqKro4ZSoYhAKGCov/a7hPBAKmlkoI6xyW0kOiU9LQ6WtoLkCyVa66ycXsSJJbK47TqowI7/kldGWwjrFMxtBREKYLDNdUMIfQ3mm2jhE7fq+Pef+xHUikf9wL+fMBqNCIVCLi8vsVqtP9D3LpVKD23uIpGIs7MzVlZWHvneuw9g1/8qFAr0ej1OpxO1Ws3MzAzRaPSJPs7vTgtZLBZEItEjEcazOoosFgtisZjz8/MnSut/2PDD8VM8BXa7nVAo9NBj17/A51FJ/Kmf+il+6qd+6ubrP/iDP+Cv//qv+dmf/dknPkev1z+x97nd3M5+dB+pUAoC0FV0FCoFqIBSoqRUKVEoF8iX8pwlztiN7GJUGGk1tbJ0vsRl5pJR9ygLZwv4dD7WL9cRIiSYDFKvr0cv1/OK5xX8cT9ioYSt5BYiRLzme5Xxowl2r3a57b7D1sUO0WyUT9V9krH9KVL5FE2WBjYD++QKeUbqhnhrbxytXEODtY57+3OYVAaabA1M7sxTa60hlU2xebZNl7eF3ZCfdC7D7aYetkN7ZAt5Rtv7GFubBwR01TUTCkQQC0X0NrUwsbqEUiZHJpdwdHKGTq3GaTGzuLWN2aBHp1Ihlgqxm43IJFK29o9x281UKrCx5+e1/gG2dgLs+0N4XRbyhSIHR9XrVDbFweE5Hnd1+GxvP4TTaUQkFLC9G6S+1oZGI2Vj8xSjUYXZpLmvhyTH6zUzO39AZ6+X3k4Pk3MHCARwu6/2hhAe9Fr49OttfG2iWqjubXOxsXtGNl+kwWsmEqt6OluNavLpLGuHl8ilIlp9lpvC82CLnenN6v35jz/RwZd//ceQSn7weenr7p1AIPCekEK5XH6iree7HyuVSggEgoesPGUyGdlsFpvN9ojN54MHsMe9b7FYxOFwcHR09ERSAB7pFPJ6vRweHt6kguDZAnvX0hf7+/s/FFEC/C0ghTt37vDf/tt/e+ixb3zjG9y6deulDDFGR0f5zd/8zWea7uzu7j622HXbdZu/3v7rmyGzSqVCsVzkKnOFAAFSsZRSuUQkGyGajVKnq8On8yEUCmk0NtIl6UIsEDPgGMAgN1CqlDDJTSyeL9JkbGLqdIoBxwD+mB+T3EyfpY/j+DHZYoZCucCod4RSvkI0G+VOzRDhzBWpfIpR3x3GDicZdN5GUBYwvjeFVqahx9XB29v3cOmrfyhCkYBWVyOnVyFimQQDdd1chVOkc5mbojPAx3ru8p3FqWodoL6difVF+txtiEVOZjbXMKg1WI0mlvd2eK1tiMOTMzYODvHYrNWN/CSAuVVPuQz+0zMavC4i8QThSJymWg9FCgTPrmhucHN+UTXeub72n2xxe7CL3d0g4ask9XU24vEMp5dxvDVm0pkcKpUGm1WAVCpheyeE2axBp1WwunaCViOnnCtykoggk4ppb3Fw7z45DPXXPmK+U6lUGOr2MrN6TKlUprPJwf5xmFQmj9epJ18ocW/+kO6BevLFEgvbIURCAbdanDcRws//eBdf/PyPIRS+fxuL0+nk4OCAXC6HTCZ75PvXns7v3tQft+Ffa4BJJJJHTvU6ne6RxyQSyUOb6sXFBRsbG7jd7hdKZz3Ynjo7O0tzc/MjP8uTOoWuXekikQhGoxF4PoE9p9PJ1tbWI/vBh5UkPnSkkEwm2d3dvfn64OCAxcVFjEYjNTU1/NZv/RaBQIA/+ZM/AeCXfumX+NKXvsSv/dqv8fM///NMTk7yR3/0R/zZn/3ZS71/R0cHQqGQlZUVent7H7tGrVYjEAhu8psPosXUglwsJ1vIopFqEFSqHrAWhYVsKUsylyRWiCEWirGpbZiUJrKlLEvBJTKFDHdcdxgPjVOpVOi0dnIcP8ar9QJgV9qpVCqYFWZuO29zED0gkopRKBdoFjbTYW1n7GicAfsgI94hxv33UEtU92W0J1GI5egVWr6x9iZmlQmdQkuJIvUWL7FMgsvkFTUGN4fnx2QKWYYb+5ncnWfYdxu73sL45hxCgZCBhk5yxTxKmZxGp4/prRUMKg0CqYDtneOqZ7NEwtbRIV6bg0KlwOFpkAaPm0giQTgao7XWx9aJH3FZRUeTj8OTM5LpDF3NdewenXJyekF/dyMb29XBtWsntnQmR2e7D5lMSPgqSXubh6OjSxLJDC1NTkLnMaLRFEODNi7DKc7OE3jcBspl2Ns/x2LRoFHLWVsP8OonO7mIZZhfPkYqEdHZ6mJytjqwNHyrasQjEAp47RMdvDldLUIPdHpY3DilUCzRUmchdJEkmshgt2gwq2R8e/kIhUxMc813U0b/09/r4J++Xvu+EMJ1nv56Q1cqlayvr6NWqx/Z+K89ncVi8UMnd6lUilqtfuQxqVT60vUJs9mMQCB4qXTWu9VTGxoeNh26Ft5792cTi8U3bm7XpPA8A2kikQiz2fzUyegPEz50pDA7O8vrr79+8/Wv/dqvAfCzP/uz/PEf/zHBYJCjo6Ob79fW1vLVr36VX/3VX+UP/uAPcDqd/Pt//+9fuB31GiKRiDt37jA5OflEUhAIBDe+ze8mBaFAiFvjZudqh2wxS7FcJF1IIxfLEQqEVKhU5TDUKuQiOZVKhavMFVaVFY/Gg0Ks4JbjFmqJmng+Tq+1l1KlhE6mI5qPshPZIVlI3hjz3HGOkEwk2AhvcJWKYlPZKAtKTPinUEtVNJgaSOZTGJUGrGoLc8F5PAY3pXKRvcsDzEoj54kwiWyS27V9TB3MY1Pb6bd03nQhqZRyvjE7gVwio9Vdz9TOEl01bdRYnCztb2E3mJFJpMztr9HqbiCcTOA/u6Slxkfo8orj0BK32jvYPPCTTGfoaW5i69BPJpfjU7d6eHNiiVy+wEBnM4sbexSKRQa7WiilyqQzOQZ7m1hY3aNQKDHQ08ji2j61rlLVq3ndTy5XpKfLx9bOKZlMno7WGk5OwsRjORrrbVxFUoSvknhrTOQLJfYPLrBatZSyeda3g2jVcjwuA3PLR0gkQnraPUzc70Qa7q8jn60OWw33eplcPKJSqdDT6mTr4IJMtkCt20gqk2dx+QiTVoFFr2RxJ4RYJOQPf/3H+PHbNczPz9PS0vKetTSWSqXHnuYfd6q/jmilUikCgYBIJIJMJkMulz/UKHH97w+i7fJBPaSXTWe5XC62traoq6t7iACu01WPIyyv18vbb79NOp1GoVA8V6QA1ZRxKBR6po/zhwEfOlJ47bXXnipg9cd//MePPPbqq68yPz//nn2GV155hcnJST73uc89cY3BYHhEG+UajYZGti63EAlESMVS1FJ19eYTihBIBdWW1XKRbDHLaeqU/eh+dTOvlJkMTBLPxxl1jzIZmKTF1MLyxTJykZyt8BYGmQGdTEerqZXLzCVioYiVWLXX/0fqfoSpwDRzwTmGa0Y5TQRZDC7xWs2rXKWVbJ5v02RpRFZSsHK6Qb+nm8XTFWxKJ52uVib2ZgDo8rbwtcW3qrMJNW18c+1tXCY3WoWahYN1bDoziWycSCRLrc1NKpfBf35Kq6cOZUXGxskR3fVN7Bwfk85mudXShrgoJJnOcLujndmNDUqlMne6OjiPhsnlCwz3tjO5uF4dMuvrYHx+laH2DkYGWpmY3azKbQ+0Mnn/2mRScbwTIZcrMnirkfnFfYrF+0SxdkQuV2Sgr4G1jQvS6TzNTQ7OL+JEIqkbchh7e4u22w3kcgXWtoKoVVJqayzMLPq/68w2s0dri4PRPh9j92Wzb3fVMLt2QqlUpq3eSuAsTiyZxWHWUOs2MrEeQCmX8J9/5x/wqcF6KpUKEomEy8vLp/omX+fpn5Wjz+Vyj83TX19fn+of3Oyv8/Tlcpm3334bh8Pxwi2h7zVcLhf7+/svPD9xrYek1+sfWzx+2gzD9VCa3++/ac99nmhHKBQil8s5ODigq6sL+Ch99LcKo6OjfOlLX6JSqTzxF28wGDg4OHjsmhHPCH+z/zeUyiVShVS1G6JSIpwJU6lUkIqlFMtFItkI4UwYs8JMvb6ecqWMS+OiV9WLVChl1D2KTqZDJamK7K2cr+BSu1i6WMIoN7J8vkydrp4OUzvxdIJ0MUM8l2DAeQuxUMRhxE+7tY2LzAXH0QA9zi62Lnbot/Vzp/YWU4fzlCtl2uub+JvlNxAJRNzydROMh1DLlNRaa5g9WMaiMVFv8fD22gw+i4tsIc/B+QmfaH2Nmc1VYqkEPXUtbJ0c4NTbaHV5WT84uLHrnNpYpb++nZGeLsYXq3MKoz1djC0uIxQIeXXwFm9N33+8v+NmoE2qFDHx9vbNVPPY9Hp1zf3rke5uvDXWm6nmO4PNTM1UPZwHbzVQLkE6nae7q4ad3RDpdJ6WZgdn51VyqPGYsBlVvHFvF5NBiVGvZmUjgEIuobnextT8IQIB6FVy9u/PNoz0+W48FfraXKzfLzzXeYwkU3lK2QImrYK/+jc/xUCr6yZPf63YWS6Xn3i6f1ye/npTf9yJ/t15+ueBUCjEbrcTCATed1KQSqVYrVZOTk5obm5+oecKhULK5fJNOuhFOoq8Xi+zs7N4vdW07PNECqVSCbVaTSgUoqmpCblc/kKf94OEj0jhJTAwMMDl5SWHh4fU1tY+do1Go6FSqZBMJh8JJ9st1SG0XDGHTCBDIBYgFUoxKoyUyt/tPtLL9NTqapGKpJQrZRbOqm5oRoWRd47fQSVWUWuoZfl8mRH3CJeZS5pNzSjFShRiBaOuUY5jJ5zmg1xlrtBmdQy5b3PvZIpmQzN3am4zezJPoVTg9frXeftgglK5hFwm41trbyNAwJ3aAQLxIAqJnGZHA1MH89i1VrwWNyvHm9SYXBRKBbKlDC2uOkLRS6KpOD2+NlL5BLFUgsHmTuZ31ymWSlgMeja3AhSKRUa7ehhbXgRArpQwNVvd1EfuEwLAUFc72VTVHWy4t/2GEIZ723l7ZomellaUCvkNIYxck0MFVBox3/ib6vXocAtjE9VW3eGhZianttFqFLQ0m1lbP6FYLNPTXcPWdohMpho5XFzEOdo7w+3QUwF2Ds4x6JTYLBoW106QSkR0tbmYnDtg5JUWat3GG0K43VXDzOox5XKFZp+JwHmCZDqPQi7kf/k/DFOKHfP223vk83kqlQoikeimACqXy78vefrnhcvlYnp6mpaWlve9zdLj8bCwsEBDQ8MLpa2uowWr1cre3t5D7anPmnbW6/Wo1WoCgcDNaz0LpVIJmUyG2WzG7/e/MIl9kPARKbwEFAoFt27dYmJi4omkIBQK0el0RKPRR0hBKBBSq69lO7xNoVygVCoRzUaRiqWIBCIKpQKFcgGRQIRMJKNMmYPYAblSjn57PyKBiA5LBzaVjWwxy6h7FLFQTIelg2wxS7qYZup0inQ+Q7lSZsQ1SiKZ4Cjhp1wGuUiOQWFg82yLQrnAiG+YXDFHqVxi2Hubb++9gVVtp8boYvJgBrPKRJOtjsWjVZx6OyKBELlERpO9jsvEFVepKC6Dg8DVGYlMisHGbub315CJJQ+0pXJz3WltpkHiZmx5sSpV0dbJO0vz9Dd2IxaKGF9cRiwS0dvSxMTSCrea2hnobGZiYQ2JWERPawMTC2uIRSLsTj1f+8YCIpGQW92NjE+v35e/aOEbb8/jsNup89lvCKFKDtXIob3dw8VZimKxzOBAHfMLhxSL5YciB6NRhc6gZm07iMOqRSIRsbl7hlopxeXQMbt0hFAA+USCmYNo9XXr9EwtV+taTTU69k8iFIpl6t16vvI//x08DsNj8/TT09M4nU7cbvf347Z9bmg0GlQqFaFQ6H3/LDqdDrlcTjAYfOHP8qB66oPtqc/TZur1etne3n5kSvlJuI4+XC4X8/Pz1NfXPyKZ8WHBh04Q74OC78V0B6BeX0+xUqRULiGoCNBJdciEsqp+kdKMU+3EorSglCjJl6qnSZ/Oh0KsYPp0mvWLddKFNO8cv0M8F+fNozcJJUPMheYwyA0IEPBqzasMu+8gEAhYji4TzccYdA5iVdq4dzJFm62Vflcv4/4JcsUs/e4eJvxTaGQq2l3NzB4tYtNaUctUSMRi6i1eCqUCx5FT9BoNgUiIq1SUwboeFv3reK0uRlr6mN5Zolgs0lvbTiKTAmC4rYextXlEQiF6vZrZ7U2kYgn9Ta1Mri0jl0oxmzRMra6hlMtor69lZm0DtUJBWVhkZfsAtVJOS72XmZUtVAo5bY1eptfWUClldLb6mJrfQioR09fZwOTsJiKxkO5uL+OT1xFC0w0hjA63MDG5hVotpavTzvTM/v1owc3a2gnpdJ7GBjOB0wjCUg67RUk6k+UoEEGnkaLTStnau0AmFdHcYGFmIYDPoWOw083afhSoejfvnsQpFMsM93h56z//MsODXXg8HqxWK3q9HoVCcXMCttvtLyUG9/2Ay+W6OSm/nxAIBHg8Hk5OTp5aS3wcHjTgCYVC5HJVJYHnKR7b7fbntvaE75KCwWBAqVRycnLyoa0pfEQKL4m7d+8+t2Lq427mEfcICrECmVhGhcqN18JuZJf1y3V2IjtshjeZDk4zF5pDLBTjVDsJZ8IUy0X67H2UK2X6bH14tB5G3aMMOAfosfXQaekkUUhQKOeZOJlk43Idl9pJi7qFZCHJUeyIekMdMrGUucACZqWZHDmWg2vYNFZMKhPpYopaUw1U4PDqCJ1Kw0UizEUizICvh42zrapCauMtZvaXKZaKeCx2xjerw2rDzX2MbcyhVskYaOpgYn0RuURKV20z9/aW0atUNHlqmN1aR6dWU+twMbu9ikmnxWOzsbS9i1GrxWExM7+5RX9nIw6rmZWtfYw6NS67meXNfcqVEj2ddSyu7qNRK2isczO3tItCLqWtycNBIIBYLKSzw83EvW0EAuhsd96QQ7GUYW29Khvd2W5jcemEYqlMZ4eDA3+ETLaIVCAilSkRS+SpcRlQqRQEQkn0WgW1XgsbOxeIxUJavBamrwXv+nxMLvoplyv8+Gut/Nc//N9jeIZshd1uJxaLkclkXuKOfG9ht9tJJpMvbHrz/YDD4SCTybyUQ5xIJEIul9+0p8KzIwXgxrjneX2jr0lBIBBQW1v7TEe3DzI+IoWXxPDwMNvb21xcXDxxjVarpVgsPlbKt93SToUKhXIBgUBQzeWL5Hh1XjwaD1allRptDb22Xj7m/Rgdlg6kIinnqXPkYjlSkZTJwCT+uJ/dyG7VkjMbYfFskUK5WpBMFpIMOgfx6r0opUo2k5vsR/YZqRnmOH7CYmiRFksLQoGA1bM1Rny3qVQqHFwdUqjkiaRjnCXO6a/pYftyh3g2yXD9LWb9S5zGQvxIx13Gt+eqnT+N/ayfbiIRiRmo72RiawGlVA6iCjPbq+hUamrtbhb2NtAqVdRYbawe7GEzGDFqtGz4D5BKxdR7XGz5j3BazKgUcnaOjnFZLcjkInYOT3CYjSjkcrYPTrAYdKgUclLZJAatEq1KwdqmH5VKhsmgZGXDz1HonKZGKyurJ0gkQtpbXaysVYXpBvrrWFkLUldrYKDfy8palRyG7zSyun5GsVimv9fH6koAm1lLU13VZOc0FMNu0aLTKtjcCaFSSmlvcrC06EcgqLamXnci/fO/P8Cf/tv/AYX82YOSUqkUo9H4yAT++wGJRILNZvtARAvXKaCTk5OXfg2Xy8Xx8THlcvm5zXBMJhOVSoV4PP7MtQ++ps1mQyQSPdfzPoj4iBReEmazmZaWFqampp64RiQSodVqH9uaKhKKaDI0oZaokYqkSMVSEoUE6WKaMmXy5TzJQpJ0IU2ulCOWi7F8vkw4G6bR2MhV9gqlWEmHuQOJUFJ1ZhMpGHGN3MxCrFyssHm5wXxoHovSSrO2GblYymkiSL6Up8XaDFQ4T13Q5+yhLChznrzglruXtfN17Ford2oHWDhe5jga4BNtd5nYm62SQP0AmWKmSgJ1XUzszHGRDNNf38nM7goGlRaP2cH41hy9Da0YNTo2jvdxmWwoZDIEkgpOY3VA6SB4is/moFAoUKZIjc1KJpvl+Owcl8VMMpVmamMZp8VAOpslcHaJw6ynVC4ROA+TKqaQSqUEQhFsFj0mvYaTYBSTUYPLYcZg1KLVKGhqdLG6HkAmE9PbU8fM3D4CATidOmbmqnr6oyPf9Ve4c7uehaXqnEOdU89JsGqyU1tjolypejcbDUpcdj1L6wEuw3Feu1XHxEL1tf7lZ1/nP/zPfw+x+PkLpA6Hg2Aw+IE4ZTqdToLB4HOflr+f8Hg8nJ2dkc/nX+h5j2tPfd7Zg2vV1ac5s13jQVIQCoWMjo4+MqP0YcFHpPA9YHR09KVNdwA8Wg/pYpp8KU+JEjKRjGQ2SblcRivRYlFYMClNaKQaZCIZdfo6RlwjGOVGTuLVU1O+nGf1cpVSpcQbR29wkjxh/GQcAQJKlRLdtm5G3MOIhSK24lscJY/x6mvoc/QycTSJSWlkxHuHhdMljmJ+Rny3mQsskivkqbPWMHkwQ7lSZrhukGwxi1goZsDXw8TeDJFchBZnAzP7yxhVetxGByKREIfBgkahZuv0ALfRjkIq4SAUoMZsJ5VNc3J5RiKfIJlJE7oKU2O2chGNcBmPkS2kuYzFiCSSNNW4iSVTxFIpapw2rBYjsWSa1voa0rkCV7EkTT434VgCg15DbY2NSgWOApe4HSbkMim7B6dkSiksZi1r68doNQrq6+zML+wjk4np66ljfvEAiVjA0O0GxiauzXcamZzaq7avDtSxuRYgncnT1uy48W52OfSoFDK2989Rq6S0NDjIpXMIBAK++C9/gt/53I+8cF7ZarWSzWY/EGkbg8GAWCx+ajT8g4JKpUKv179U5PJgbcHv9z9X+giqG71cLn+oHvG0tT8MrmvwESl8T7h79+73VGwe9YyilWrRSrUoRUokQgkqmYrz9Dk7kR12IjusXqzyzvE7jB2PcZG+oCKo4I/7iefjNJmaOIweohar0cl0dFm6aDO1Meoepd3SjkfroUiJ8ZMJJgOT6GV62tVtJAsJ5oMLaKQaFDIZ4/7qz+DU2tm/8kMFhr232Q8fIBFKGPD2MbE/TSQbodlWz8zhInqFlnQuxdFlAIvaiEQoZjt0QCQeJpPNcnR5ikdvI5aKcxoN0mBzE07EiKYStHnqCMYuMWo0dNU1cB6Pkspl6W9uZSd0jNVopL+1BX/wjGQmQ39rC/snp6jUUnrbGjg8CRFLpOhqriNwfslVLIHHY+AqkuD8MkpDrZNMrkAgGKbGZeEsfEU8kcFq0WE2a1nfOEGrUdBQ72BuYZ9sLk9Xl4N71wqodxpvyGH4TiPTM/sc+S/5+GgT+4cXxBJZGmot5HJFjk8jmIwq7FYdKxsB9nZD/Mn/5R/ziz9956XuKZFIhNVq/UAUnB8UyfsgwO12v3TB+bpGkEwmSafTzz17cJ3Se1Al4UlrfxgMduAjUvieMDo6ysLCwlPt/3Q6Hblc7rHFww5LB7lSjkQhQa6UI1fKIUCARWlBI9UgFUkxKUx0W7v5mPdjtFva0Ug1aGVaem29GOQGwtkwerme3cguyxfLXKQvGDsZ4zJ9yXH8GH/sEK/Oy23XIM3mJtaS6yydL9Ln6EEtU/Pt/TdwqO20W1qZOJ7CrXbQamxh4nCao8gJDQYfM/55NBIV0WSUw8tjTAoDUqGUg6tjWu11lCtlzhKXNNpqCWXOKVZKdHtbCGfiJHJpTEYD6WKOVC7DYHMn26d+MvkcTquJtcN9svk8Q+2dLOxskSsUaKmvYWFrm1yhwFBnx821UFphZeuATC7PYFcLG3tHpNJZ+tob2Q8FiCXSdLb6CJ1fEb6K01TvIpnKEAhd0dXtQSQSsn9whsWsxXw/ctCo5TQ3uSiVy4hEAgYH6m6sOkeGG5m4f33ndj25VJ5srkhnq5PQeZzLqyQepwG5TMLuwQUatYz/1xd/hn/wI53f0311rez7QUkhXV1dkc1m3++PgsVioVKpvJTG0IPtqZFI5LkjBaFQiM/n4/j4+GaO5ElrP4oUPmD4wz/8Q2pra5HL5fT39/POO+88df2f/umf0t3djVKpxOFw8M//+T8nHA6/0Hv6fD4sFgtzc3NPXCMWi9FoNE+sKzQbm9HL9GhlWgxyA2KhGJFAhF5efUwilFCqlMiWslykL5g4mWAhtIBYKOY4fky+lMej8+CP+6nX1ZMv5+mz9aEQKbhlvVWdkC3kGDseJ5/NY5AYaFA2kEgmCSaCOOV2jCI9qxfr6KUGKFdYv9zEKDdgUZtQyOU4tXa0Si2BVJChhj6EYiHnqUvanc2IFCLCqSi93nZOroJcpWOMtPaxfrJLOpfhTlMvC/vreG1ORtp6md5aoVgqMdLey2EkQKlcZrSzh3trK5TvXx+en1Aulxnp6eLeymr1uruLdxYXafA5Ge5tZ2al6tw21NPG0uYeeycBPjbaydbuCclUlu72Wk5OL7mKJmlpcJPIpgiGIng9FsRiEfsHZ5hMGmw2PatrR5wEwtR69UzP7CMUChi6Xc/4u1JJm2snDPZ42do9I5nK0VRvJZ3JEwhGsZo1fP3/83levfO9O5cZjUYqlcoTI8wfJORyOSaT6QPh4SwUCm8Kxi/z3OvI53lTc9e1h2vPlKdFbx9FCh8w/Pmf/zm/8iu/whe+8AUWFha4e/cun/70p58Y8o2NjfEzP/MzfOYzn2FtbY2/+Iu/YGZmhs9+9rMv9L4CgYDR0dHvKYXk1DhJ5BPEc3EShcSNbHYinwBALpajkqiQCCVIBBLajG284nwFtVCNFCkt2hay6SxChMjLcpbPlzmPnvNO4B3O4meE0iEsUgu1ah9SkZREPslGYhODxsCQ6zZn+XM0eg2tlmbEIhFrsQ2aLQ1IJBL8sWPUajW5Up5ALEiHo5V8JcdFIkxfTSd7F4csB1a509DH8vFmVTm1qZ9YLk6hVGS0tZ/J7eoUtk6jZHx9AYCR9j7G1xY4jZ7TU1vH2Mpi9fHOHsZWFtk83ue1W703khcjPV2MLy1DBep8diYW1qoaSP0d3Ftcp1QqM9zXTr5SIF8oMtjbxPp99dSe9jr8gQumlzfp760jnkgTDEXwuE3VE/5eCKNBhdGoRiQSIpWK6Omu4d7Uo6mkpjormUyefKFEV5uLQDBKOJKi3mvmO3/5K3S3vTeDXtepjg9CCgmq0cLp6ekHInJxuVxcXV09NTp/Eq7VU2Uy2XMRw4NtptdeC0/6f/ARKXzA8MUvfpHPfOYzfPazn6W1tZXf//3fx+Px8OUvf/mx6+/du4fP5+Pzn/88tbW1jI6O8ou/+IvMzs6+8HuPjo4yPj7+1DVPEserVCrctt9GKVSiEqqQV+RIyhL0Qj35TJ6TqxN2z3dZOl1i/HicqdMpjiPHXCWv2AhvsB5ZRywUs5/ap0wZuUKOECH11no6LZ10ujoZcg6h1+o4SB4ydT6FWWXGq/CCsMy9wBTFchGZSMre5SGXqTBNlkaUUiVniXN6XF1sX+5wlY5wq6aHnYs9VkPr3KnvZ/F4jWwhR5enjWQuRalcYrRpgIntObbOdhlt7WdsoxpBDTf38ebGPZRSOUMt3YyvzSMUCLnd0kVFWEEkFHK7rYPxlcXq420d5IuF6om9s+M+OQgY7upkbf++RWZ/B+P3JS9G+zuYmF8jED5nZLCV6YVtCoUSg33NrG75yWRydHf4kCvFRKIpmhodpNM5AqdXOJ1GVCoF2zunKFVi3E4d8wt+xGLhQ6mk0eFGJu7topFJGOz1srETIpXO09vh4Vt/8SvU1phf+N55GhwOB+fn509NWfygYLFYKBaLH5jI5VoP6WUgEAhQKBQkEolndlU9uNE7nU5yuRxXV1fPXHv9Ph9WfOhlLvL5PHNzc/zmb/7mQ49/8pOffGJn0PDwMF/4whf46le/yqc//WnOz8/5y7/8S37sx37shd9/dHSUL3zhCw/dFO+2EMxkMqRSKVZXVykUCg+pWxbLRc7CZxSozisUBUVEAhFyqZyisEiikKBMVQjPrrajkVUlM7QFLS3CFpRiJRKZBLlIznnmnDJlrrJXrFysUKHC6sUqGqkGsUBMp70Ti9zKN/a+iT/tp8Xchkqq5K2jt6nTNeLQ2Jk8muKO+w53vINMH89RKpf4ZMsn+ObmW1QqFQZqeglH49WUTsNtxnemGakdYrixn7HtGYQCIU3OWq6iMSQiMT21rUxszSMTSxlq6+I7i9PIJVJaa+qZ2lymyeaj3uFian0VuVRKq7eWqfVVempb6Wlu4t7KKhKxmJ7GJiaWVhEKBbx2e4A3p+7bevbd10OqgNNu5Hi3mm8eGWxlfHoDgMG+ZuaXd2mr99HV6WVvP0QqlXvIfMdm1ZFO5zgOxFEppTTU25ieqbas3nmgK0lcqTCzGqBQKPH6SBN/9uXPoFG/9+JnWq0WqVT6TOXUHwSEQuFNwfnaZ+D9hNvtZnl5mfr6+hfWQyqXy0gkEoRCIWdnZ0/1aH+wS0kkEuHxeDg8PHzEsfFx9p4fZnzoSeHy8pJSqfTIH47NZnviENDw8DB/+qd/yk//9E+TzWYpFov83b/7d/kP/+E/PNd7LiwsMDs7SygUIhgMIhQKGRoaIhKJ8Hu/93totdob2eJrbRuxWEypVMJsNj8icvYt0bc4jh5ToQICKJaKIAALlmoBulhthxMJRVxmLtm43KBQKtDv6Gc/us9R/IgR9wh7kT18Oh+b4U2MMiPlcplh1zClSol8Mc9CaIEB+wAAXcZOdCo97/jHUUlUNFkb+NrmNwGQS6R8e69akxmtvUO6kKmma+puM7Y/xV3vSNWzeWcaiUiCTCLmO5tTVT8FZwNTuwvcrbuDSFjPzO4KWoUaj9lBtpRFp1LjNFpZ2NtAr9IgEEMwFEarUuMyW1jY2UKrVFESFNn1B1ErFNQ6XcysbVRJo85HsVysaiO1NzIxv1bVOupuY3x2lZGOHjxOC+M3AnnfJQeZUoTfHyGVytHR7sHvvyCRzOKtMZPLFdnaOaWzzUcqXWZp5fjGr3niXjU6GR1u5O13tugZbqKhzsr/49/9U6TS78+fkEAguJG9eL9JAaon5ampKQqFwks5Fr6XMBgMSKVSzs7OHlI/BZ6qMpvL5cjlcqRSKYxGI36//6mkcE0g16ipqeGtt956RMr7OuJ4v8UD3yv8cPwUPBquPU3Wen19nc9//vP8zu/8Dp/61KcIBoP8xm/8Br/0S7/EH/3RHz3zvd555x3++3//79jtdux2OzU1NQwODvLJT36SoaEhdDodYrH4offf3KzKKng8nkdez6P1sH65TqlcolwpU6lUiOaiSIQSFBIFIoGIUqV0I6VtUVjw6XwopUpEAhF1+jqkIik9th7McjORbIQaXQ2L54v02npZOFtg1D2KVChFJpbh03pZjqzQL+unxdxMKp8ikDhBJVHSYm3m23tv4NF5ceocjB1M0mxqZNDbx/j+FDKxFIlEzDubk6ikSuqtXr6zNUaTvRmRSMSCfw2jSl/VK/JvYdEZ0SrUrB3v0GyvxajRs3G8j01vRiGTsRU4pNveSiSZYsN/gEVvQKNUsrK/w93WQUJnEVZ29m48nBc2t2n11tLW4GVmeROpRExXUz2TC1UhPKVGzDe/WU0rjQy2fZcc7vsuDLV3UuOxsLJWHUprbXYRPIsSjaZwOo0oVRJW1gIP+TULBDA0WH8TLfyduy184Td+7Pt+MnQ4HBwcHHwgNmK1Wo1GoyEUCj32Hv5+4lpe/MENXqlUsrOzQzgcfqy8+Lv9IqRSKSqV6uaAJpfLmZ6eJhaLPXHI7N0pIblcjsPhwO/309bW9tA6eD411Q8DPvSkYDabbyYVH8T5+fkTT1i/+7u/y8jICL/xG78BQFdXFyqVirt37/Kv//W/furpAeDzn/88n//852++1mg0LC0t8eM//uNPfM61v8LjcMd1h7cO30IgEsB9HtHL9eRL+ZtIIVlIchI/IV/O49P5KFNm8WyRUCrEkHOI6eA02UKWXnsvsVwMlVSFAAEGuYEh5xBysRyZWMbYyRithnYUQgVSoYTVyCG5Ug6pUYZb72YusIBeoaPJ1sC3t99CK9MglUjYuzxEp9Dg0rr4zvbbNFgbEQqELJ9sYNNZcJlsvLE2idNgQyQQMr4zQ09tN+exMHuhI7wWJ7FsAq3YiM/mJJPPcXgWwGdzIpaJONo/o8Zqp1Aqsn8awGW2IhYL2Dk6xmYyopDJ2Dg4xKjTUqwUiV5F0agUeB12Zle2kUkltDf5+ObELG6HC4/ru9HC6O02xqaq1xqdmG9+vWrE09tTy+ZmgEw2T32dnVgsxfLqESajGr1ew+raCTKZmPY2N5P3C8//x9/5B/z6//R3fiA5Y6VSiVar5ezs7H1XK4VqtHBycvKekcLT3OHebSJ0LS/+oFdEoVBALBZjNBqRyWQPfe9pG3S5XKZYLN5s8NemOI/7fO9+Ha/Xy/T0NI2NjTdE/TjP549qCu8jpFIp/f39fPOb3+Tv//2/f/P4N7/5TX7yJ3/ysc9Jp9OPhHrXv9CX6bAYHR3ly1/+8lOjE71eTyKReOypr9fWS1lQbR2tUKnOKwgECAVC4rk48VycXCmHQWFAL9OjkWlI5pM38hY6uY5eWy8qiYpUPkWvtZd8KY9YKOYwdsh+dB+RQIRCqEQr1VJn8HESO2Hy9B4dpk40Mg2LwUXajJ3UGnzkS3miuSh2jQ2FRM5KaJ3XvK9wGA6wHtrCbXDg1Nl4e2sKr8lNrpgnko1Qb/USzyQ4TVzR5KhDo1SyeLDxkM9CR1srM5vrxFIJWty1hK7CnF5cUmt1EMukuUrEqXd5iCUTzOwsU+9xkUpnODwN4rSYEQmF7Bwd82rXLU5OrljdPkSrVuJxWJlf3UEmk9De5uHr374vy93ffEMIo7fb+Pa9JbRaPS3NLmbn9iiVynS213DgPyeZzFLjMaNVq1hdP0erUeB2G5hfOEQkEvKl3/8Zfuafjrzw/fG94DqF9EEgBbvdzvb29lMtJ69P9c+z0ReLxce6w8lkMtRq9UMb/fUJ/0FsbGxQLpdxuVwv9HNcb/ROp5PZ2Vmam5uRyWSPrHtcR5FOp0Or1XJycnIjm39NHh9mIngQH3pSgKpP8z/7Z/+MW7ducefOHf7jf/yPHB0d8Uu/9EsA/NZv/RaBQIA/+ZM/AeAnfuIn+Pmf/3m+/OUv36SPfuVXfoXBwcFHcpTPg8HBQc7Pzzk6Orpxa3o3ZDIZSqWSaDSKxWJ56HsSkQS3xo0/6keAALm46s0sFokxyo1UqFAql25sOuO5OGuXa4gEItxaNwuhBc7T54y6RxkPjNNiamHzfBOD3MB+dJ8mQxMGhQGdVM9b/rfYjx2QKCSwyqy4dE6+vlOtJZjVRjbOtkgX0hgURhDAwZWfenMdZUGFw/ARjdZ6rlIRMqU0rY5GgrFzoukYFrWZRDbFReKKrppW9s78KMVKempb2QockMln6altIxg7+64T27GfTC5Ld10zmWiBq/M4HXX1+ENBEuk0rTW1qAQa9o4D1HtcxBJJLqMxPDYrxUqBvaNTLEY9GpWCtZ1DtBoVbruZk4uzalqpzcfkbDVtNzzQekMOw6ON/M3fVAvVA331LK36yeeLNDc6Ob+IodOpMBoU6HQq1jdOUSik/K//6Rf49Ke6X/je+F5xvRFnMhkUiqerrH4/cX2q1+v17OzsYLFYHtroH9zwK5UKYrH4kY1eo9E8tNHLZLKXcoe7htvtZnp6mqamphdOr123p16rpzY0NDyy5kkaSV6vl83NTbxeL0Kh8IeqHRV+SEjhp3/6pwmHw/yrf/WvCAaDdHR08NWvfvVmgw4Ggw/NLPzcz/0ciUSCL33pS/z6r/86er2ej33sY/ze7/3eS72/Uqmkr6+PiYmJJ5ICfHde4d2kANBgaGA/sk+pUqJcKlOhQjQZRSQQoZKqEAqElMolEvkEh7FDypUybea2G2/nQccgcpGcYdcwBnk1olBL1VV/BYWBqdMphl3D98X1ooy6R7gXuMdeZA+5SE6fo5eVsxXShTSD7lssh1Zo1LdgV1vZudznInFBr6eT7bM9Uvk09SYfgUiQeDZJv6+b1ZMNOmwd+CwuFg7XKJSKyGQSNgN+Mvkstxu7mdtfo1gs8mrnCOOrCxRLJQabO1nY26DVVkeHt47toyPyxQI9jS1s+Q/prTXQ0VCH/zREIp2myevhMhJjYnWF9sYmrmIJ9o+DWE161EoF6zt+tGol3R31zCzsIJGI6OmoZ2KmWmweGWwjeFkdUrx2YKtUKnR3edneCZLJ5DEaNYjFQg4OLzHolfzln/0yQ7cf3TR+EJBKpZhMJkKh0BMNnV4WlUrloZP70wq0157PYrGYQqHaKXe9wT/OCvQHsUlqNBq0Wi2np6dP/bt7HK7Nc5xOJ9vb29TV1T2SKnrSZm+z2dja2rrpXnoceXyYo4YfClIA+NznPsfnPve5x37vj//4jx957Jd/+Zf55V/+5ffs/a/F8f7JP/knT1yj1+uf2F895BriO/7vICgLyJfyCBHiUDsolAsIBUKECCmLql0ObeY2ZCIZEqGE1YtVwtkwtbpa3jp+C5FARKOxkZWLFe647hDJRhAgwKgwIhPJ6LP3sXi2iEvlplgpIRNIqTPUMXF8DyFCPtbwOt/ZfRMAt97ONzbfpFQucbtmgFQqSyqfZqj2FjP+BdrMbahlKqb2qwNqFq2Bry+9U1VRbbrFxPYst1x9yMQyxjerMwsjrf0UcoXqVHNbDxMbS1QqFRRKGbOrO5TKZW63dTC7sUmpXAJRmd2jE7L5PF2NDeydBEhlMjT7atArVKztHOJ1WskXiuwfBzEbdOg0KiRSESqljHqfg5mF7Yec2UQiEa++0sNbb1cjh9sDjcwt7FMslmhtcXEajOCwmhCJxPy3//JrtLa8ePT4XsJut3NwcIDP53vmZnPdHvm0Df7Bf6HaNfPuVM2TPJ8BJiYmsNvtz6y9/SDg8XjY3d2lpqbmhTbi6/ZUo9H4xPbUJ7WZXg+zXXcvFYvFjyKFj/Ao7t69y2//9m8/dY3BYGB9fZ1isfhIfvRamiJVTiEUCMmVchTzRURCEZFcdcK5UC4gE8nQy/UIBULO0meEs2Hq9HXkS3l0Mh1tpjYypQwjrhGkIin9tn4S+QRXmSveOHoDp9JJuVJGLVPTrm9j7Wqd244hnBonOrmWXDGLUCDkTs1tNsPb1aG02juMHUwy4hlmtP42Y3tVuXC3ycHfLL0BwGjjIPPHy1QqFUabBhjbngHAYtDzNzNj1TX3B9q6PW2Pten0mtw4LXYm11YAuNPRxb31FZpcDWhVShY2dygUi3Q3NbB9dIzKo6KlzsNZOEIklqTGaaVYLLF3dIq+VYvTbmJ5/RCFXEpzg5up+aoD2+2+JnLp6oY4cqf5xpntwcJzd2cNv/dvPv6+EwJUlVPX19cJh8NIpdJntlyWy+WHTvLXG7tcLken0z2S1nnRrhmXy8Xp6ekHghSsVitbW1tcXV09Mj/wLFwTg9vtfmx76tPSQi6Xi52dHaLR6HNLcX9Y8BEpvEcYGRlhc3OTcDj8xJvzesQ+Fos9skYqlmJSmkjH0wgFwqokRTaBWqbGprLhUDsQCUQIBdWCVr6URyaS0WHuwKQ0sXK+wlX2ihIlZoIzdFm6WL5YxqV2EUgGqNXVEs6E6bZ1Y1Za2AxvEIxXTWUMCj2rZ+ucJk7pt/fTbmtj3D+JSCDilfpR3t6rTmwrZHK+tVadXxiuG2Tz/L7NZcMtxnamESDgY+2v8J21CQQIGGrsZfpgsZreauy6mXDWqBTMrd5vFW3rvSEHp8V8QwijXT2MLS8CUFtj52tvT1OpVBjsbGN+fYtiqQSiEpeROJFYkqZaN5dXMa5iCdx2MxexK2KXJfRaFXabgcXVfSQSEd3tdUzMbNDb2sjInRbGJ6s1h6HBRmbuF56HBhv5yn/4LHu7G9/XfHGlUqFYLD7zRH+90S8sLCCRSB45wev1+kc2+ne3RL+XcDgc7O7uvu91DnhYD+llSOFaUmR/f/+R9tSnbfYSiQS3283h4SFWq/UjUvgIj8JisdDc3MzU1BQ/+qM/+sR113WFx93AneZOzlPniAViCuUCapmaq+wVYoEYhURxU1eI5+Mcxg4RIKDD0lGNBLJXNBgaOEueoZfpsaqs9In6sKvs1OhqUEvUHMYOucxcsnx+X1PIPcrhpZ+pwBSpfIpOWwehVIhwPIJRYcChdVAo55GL5bTbW/jWzndw6WtwaG1M7E8jEUoYaRxkfGcaqUhCp6eVfClfva5pYXJnHqlIwmjrbd5am0YiEtNd28rY5hwDvj4ECBlfX0AoEDLY0on/vtbPSGf3DSGMdvWwfrxXHZ7r6WR8sUoatzvamNvYotfXgctmYsd/SjqTpcHnIhJLEI7Eea2nnwP/BZs7J2jUCrxuK7OLOwiFAhRKEUuzh9X3e4AcPv2pXv7k//nLKBRSjo/2CIfDWK3WF7oXyuXyMztvrr++9gF+90avVCrR6/U3X6dSKba3t3n11Vff93y1TCbDbDZzenpKfX39+/pZoFpwHhsbeymSelA99d3tqc86EHi9Xt555x20Wu1HNYWP8HiMjIwwMTHxVFLQ6/VPnLTusnfxtYOvUSqXyJVylCol9DI94UyYeD6OSqxCLpajlWoZdAyikqoQCURcpi9pM7VhU9mYCEwgF8s5jh+zdbXFgGOAmeAMfbY+KlQ4TZ4y5BwikouAsEIgG0AukvOJ+o/xrb3vAPC692Nsnm+xdrbObddtvAYPcyeL6BRamu31fGdzDK1Mg8fookIZrVyNx+Ri7nCZTkcrjY5a5g5Wqo8bXZQoopYrqbV5mN1dQSmVY9Rr+PrUPWQSKe2+Bu5tLCEWiuj0NjC+soRAIOBOe2eVHCrw8dvDfHvqfl3iAXLQGxW88c4uxWKJzuZaDo5DJNMZaj0OihTxH59jNmrR61SsbvqRyyS0NdUwMbfJ7fYOxELJDSH8s//hVb70f/vMjVOa1Wrl/Pwcq9V6c6p/no3+wQGqd5/grweorr+WyWQ3omtPg0ajYWdn56XSJN8PuFwuNjc3qaure983QLlcjtlsJhAIPLaL6Gl4Unvq80hXKJVKLBYLl5eX7/tw4XuJj0jhPcTdu3f5yle+8tQ1BoOBra2tmxPig7hlv4VaoqZQKiAXyymUChTLRewqO9FclGQ+SbKQRCaSoZNXw9xgMshedI8WUwvRXJRcKUeXpYuZ0AwOtYNcMcegYxCZWEanpZON8AYaiZat8BYKi5JuUxcnyQDZYlUvf6TmDsVKgWAiRKO5gbPUGSfhEE6tA4lITCIfx6axoJIpWQtuctvTj1ljYi2whUVjIl3MEImkMGuM6ORa1k626XS1YDdYWPFvYVBpsWrNzOwto1NrcJmszO+so5TJaXR5KacqSEQiuhubmFhdrs4atHeQLd6vAfR2Mb5QjXSGe7qYWltGgJCBrmaWNvbIF4q0NXgJnF1yErygqd5LKpVl9yCITqPC6TAyv7KHSCTEYFLwta9Wp59/+X/8FL/6y58iGDy92eRTqRTRaJRIJPLQANXjNvpr6YXrjf5ZA1QvCqFQeOOz8EEgBZPJRLlcJhwOYza/t2KALwOPx8Pq6upju4iehev21OtGkPr6+pt5pWelhXw+H7Ozsy8cTX6Q8REpvIcYHR3l53/+558axiqVSsRiMbFYDIPB8ND3ZOLqZn8cP6ZYLlKqlG6G1HQyHRqphkqlglQkvfFZMCvNuDVu1FI14UyYLmsXGpkGpUSJS+1iNjRLk7GJ7eA27eZ2iuUiVpUFo8LAZSrMQcRPoVwgU0rT6+hh/GiSGm0Ntz0DLAWXyRZzvF73Osuna5zGgyjFyqoy66Ufr9FDKHlOKHKF1+QiXyyyd3HI6w2vsHVywN6ZH7fRTiQTJZ8Gh8GCRChlK3CAVWei0eNjamMFo1qLRW9kaX+LRqsXn83B7OYGMomEjroGJtdWaPXUMdTVcUMIo71djN2//tTIKN94e45KpUJ/RyNrO36yuTyNXic6qZztvQAWoxapVMTG9jFymRi33cS3xhdQyBX805/u49M/4uXg4OChjV2lUpFKpXC73dhstscOUP0gYbfbmZubo6Wl5X3PYV+L5J2enn4gSMFoNCIWi58pcvc4XEc6LpeL7e1tamtrHzul/DhcW5Y+y67zw4SPSOE9RF1dHSaTifn5eUZGHj/5KhAI0Ov1RKPRR0gBoNXUynnyHIVIQYUKOpmOTCFDvpxHKBBSqBRIFBJEs1H8MT9ykZx2SzvRXJSl8yXaze3sRnZJF9JIRVIAHGoHMpEMj9aDRCQhlouxdFbdUHusfRRSBbbD21ASIRVKcemcHF0GyBZz3PYMUKRIOH1Fl6ODg6tDvOo6dAotgViQWCbOxxtfY96/SiQdo8lWR6Fc4DRyRoPdRyQZI5yM8ImWV1je3yYYO8VrcZIvFpFIRDhNFsQiMVsnh5i0BkrCEheRGFqlCo/NxtxWlRwUCik7B8cIBAJutTbfEEJ/SyNn4XMqlQodDR4W1nYpVyrUuSwcBS8Q2UQ4rDryhRKBUBydRonZoGX38AyJWMT//Q9+gX/wk8NPTIFks1nS6TRKpfK9uEW+J1y3iV5cXGC329/vj4PT6WRycpJ8Po9UKn1fP4tAILix63xRUrguOD/Ynnr9t/msqEMgEKDRaIjFYg8pGrzfKbXvBT8cCk4fEFyb7jxJsvsaTzPd6bH3kC/nSRVTRHNRwpkwmWKG89Q5u5Fd9iP7bIe3OYweYlaY6bH2oJPpUIgVjLhG8Ol9uDQuRtwj5Eo51BI10WyUlYsVDqIHLJ4tsnq5il1tZ8Q9gkGuZy2xRqKQYNDdj0vnZPL4Hj5jDSPeO0wdz3CaOGXIO8D62SaJXBKXwcb+5SGxTJxedyeFSoFIOka3p42TSJClk2V6vG2EoheEkxHa3U2k8mnOY1c0u2qJZ5IEI+dkiimKpRJH50FcJitSkYj90Ak+uw2NUsnawT4quRyHwcT89iZ2g5oGp52Z9WoNoKu+lrnNHQ7OA9zqaGR195hypcKtjkaOQlfk8gWkSgmlioBwJInTbkKrUbPnP0OtkvNf/t9f4B/+vZGn/gHbbDbOz8+fqb3/g8C1cuqTalI/aKhUKnQ63Qfm8zidTuLxOIlE4oWfe735X7enXg/rPU8qSi6Xv7RN6AcRH0UK7zFGR0f56le/+tQ1BoOB3d3dx9YVBhwDiAViBBUBMmlVj0UoEGJSmsgX82SLWdLFNIVSAZlYBkLYvNrkOH5Mp6WTWD7G6sUqQ84h5kJz2FQ2NsObyEVy8qU8o65RMqUMgrKQ8eMJGgwNqMVq6jV1ZEtZDiKHmJVmlFI539x+ExBg01jZDR1SLBcZ8Q2xF94nW8zdDLHZ1FYGa3uZ969QLBcZ8PWQTZVIZlN0e1rZDFbF5DrcDeyeHZEt5Kk1u1g/2UVZ1uLSm4mnkiSyaex6E0IRBC4vMGl1qORyDs9DaBRKbA4z35lYQiIW093UwOx9cuhoqiN6Xq05DPe3MzG3BkBfeyPru346PE1oVIqqd0L4CotZx//vj79Ab+ezO2d0Oh0ikeiJHWM/aFwrp34QTudQTbn4/X48Hs/7fjqWSCTY7XaOj48fUjF9HlxrF1mtVvb394nH48+doiuXy+j1eg4PD7FYLO/7/4fvFR9FCu8xRkdHmZqaeqpjllqtRiAQPPZEIxfLsaltlAQl0oU0yUKSYDLIWfKMTDFDiRIykQyNTINEKOE8dc5x/JhabS02pQ2pSMqQawij3MiIe4Reay9urZsWcwt70T2ypSxzoTlkYil6mQ672oZRaWQpssx+dI9+Zx+lconx40mMCgO9jm4m/PeoN/sY9g4xfjDFbnifEd9t7h3MUiqXsKvMnFwGKJaLdFibmD1copQv0GqpY+Vkk1wxT6PFS6lcIlvI0+lpJBA9J1PI0dvUQjSbIpFN0+yuJVcssHl+gNtsRiqRcHR+hlVvwGIw8M7aAjajgWZfDbPrm4hFIgY72hhfXEGnV1Yd2O4TwlBvK4sbe2RzeTQGGecXMS7CMWprbHz7r/7NcxECcLNRnJ2dvdwN8R7jQeXUDwJsNhuZTIZ4PP5+fxSgWnAOhUI3HWAvApFIhFgsxuFwEAgEnpsUSqXSTfT/MlHKBw0/1KTwh3/4h9TW1iKXy+nv7+edd9556vpcLscXvvAFvF4vMpmM+vp6/tN/+k8v9J7d3d2USiXW19efuObBusLjUGeoo1y5b9whEGNWmtFKtSjECnRSHVpZ9bpQLpDIJzArzFjVVk5Tp8yH5skUMsyGZhk/GSeSi7AX2UMlqZqCKCVKBh2DiIRi0sUMY8fj2NU29BI9FpmVs8QZkWwEi9yMW+li4XQJuVBOIV1g4nAKAQLajE3EUtXP3mPvYD64gl1vZbCmh9XzbSpUsFnNbFzsU74vebEa3MFg0HKnuZe1kz3yxQKDDV1cZSKkshl66ls4uggSScbx2Z2oZDKC4Uu8NjsikYj90wA6tZrmuhpWd/dRymW019cyvVr1UZAphFUHNmD0Vgf3FqoKmrc6m1ne2SGby9PVVsu3/urfUO97sZzzBymFBNVo4YOSshGJRNjtdgKBwPv9UYBq3UWtVr+Uv/WD7anhcPi5T/ylUukhr4UPO35oSeHP//zP+ZVf+RW+8IUvsLCwwN27d/n0pz/9kDDeu/FTP/VTfPvb3+aP/uiP2Nra4s/+7M9oaWl5ofcVi8UMDQ0xOTn51HVPqyvcdt5GKpQiEopuNv5MKcNh/JD5s3mmT6cZPxlnPjRPuVLGp6tq4mxfbaOVaDHKjRjkBkacI0iQMGgdpFQoYZVb2b7cZjoww9v+t9GINGhEGirpCulChuXwCkaxgW5jF6fpIBKJGIfKjlVjZjO5iU6mpcvZznpkG6lKwqC3j8XQKgIEmI0Gpo8WARhpGOCN7TGcBhsjzVUNJAC5TMLkVlUnabilj5m9FZaONhlp72X1cIdMLnufHEJI5CLqHS7i6TTB8CUeqw2ZWEyulMWo1eC2WVna3kUmldDb0sQbc3M0+JyM9LczNlslh+G+NuZWtwlH4/zjf/gKX////ivs1keL+8+CXq9HIBB8IDyKoUpSsViMTCbzfn8UoJpCOjs7+0D4SQM3BeeXkcG/bk9Vq9XPfQi4nmfw+Xycnp7eaEp9WPFDW1P44he/yGc+8xk++9nPAvD7v//7fP3rX+fLX/4yv/u7v/vI+q997Wu89dZb7O/v3/jQ+ny+l3rvu3fvMjk5yS/8wi88cY3BYODw8PCxHgwDjgHKlCmVSwgFQvKlfFUmW+2mrC5TLpWhfF/psSKgVCpxnjpHLpBjk9rYOd/hJHuCSCViPbWOXWbnLHeGSqQiWUriUrkxyo1YlVbeORljP79PvpLHobBjMVr49l5Vz0ilUpK8SpJIJXFqnHjUNUz5Z9HKNQiEsOBfQS6W0eZo5tvbb6NX6mmy1TG+O4NAIKDL28zXFt8GYKT5Ft/ZmKDeXo/DYL2RvBhq6aKQrgrk3W7pYm5njWKphFgm4PT4kkw+R5PHy2UswlU8jlwqR6dRs+0/RqtW4bZamd/YQiwS0VDr5GtvVAlotL/jJnL4B58a5X/5P/0iMunLDRhdp5DOz88/EHWFa+XUYDBIXV3d+/1xbrqiHmeP+X7AZrOxvb1NJBJ5YU/p67/Fa0ntx9X93o1SqYRYLEaj0dw8r7W19aU///uNH8pIIZ/PMzc3xyc/+cmHHv/kJz/5xM6g//pf/yu3bt3i3/7bf4vL5aKpqYl/8S/+xUudxp6nA0mj0VAul0mlUpTLZTKZDLFYjPPzc8JnYcwCM+Qgn85TyBQ4i51xfHHMZfiSq9gVkWSEWCpGJBPhIHnAdmIbjUyDQW0gkA2gkWpQa9V4dV66nd3ccd3hrvcuraZWvMYaVsIrxItx8uU8IqGIj/le4yxzztjxGFqZlpGaO7ztfweFREGnrZ1MMY1ELMKpdWBUGpg7WaSvpgufqYb542UUEhm93namDxaQiaX01nQSSpwjFooZrO9hfGsWAQKa3L4bQhhp7Wd8Yx6BqMJIey9Tm8s35LB6vIdFq6WrvpGTizOu4lXznXg6iVatwmY0YNLpWN8/uJ9KqmP7pBq6D/e13RDCL/6TH+eP/+2/fGlCuMZ1CullTp/fD1x3If3/23vv+LiqM///Pb03zWg0Tc22LMuWiyy5yJIxgWCWDQlJNgF+JIReFkiWsKQAr2+WsAspuyHOl8ROKAtklxBeIZBkNzQvfDHuXdiyZMlqVhv1Lk2f+/tjmFl1W7ItjfF985oX1r3nzpyZuXOec57zPJ8nGfojkUhwu91J40KSyWQJPaSZEg9P1Wg0SCSSs9q7GZ35HFdPTRZX42z4VK4Uurq6iEQiE8pxpqWlTemLraurY9euXajVat588026urq477776OnpmfG+wrp162htbaWsrIxwOExaWloiwWW8bPH+/fsTN9AYkTO5mbpoHYL0f4vtDAQHCBPGorGglquRSWREhSjGqJEcWw5quZqh4BDpxnScOicne07SH+jHprFxuO0wG9wbqOyuZI1zDRIkSIhJdh/2HiYQDRIlSpYxkxSNjd2Ne0ECRZ4C3q1+n0g0QpgI/rCf1gEv6WY3OpWG/fWHsemtmDVG/BFfrGSn2cWR08exaEyszMrjQG0ZSrmCFRl5NPQ0IkHCutyV7P7EOKjVCnYejRW9KVlWwO4TRwFw2MwcPVVHKBIZU3xnqSeH9q4e6ltaSTEasJktfFxVg0IuZ+OaVew8GJPA+ME3b+a7d994XqJBLBYLgiDMavZ5IbDb7VRWVjI4OIjRaJzv7uB0Ojl16tSEovbzhdvtZs+ePfj9ftRq9VlfF5cziV83mXrqeEZrJKWmprJ8+fKLOgLpU2kU4oz/YqYrlxmXG37llVcSSolPP/00X/nKV/jVr351RqGt1157jVdeeYW2trbEDK6kpASNRsOPf/xjVq5cmRjw9Xp9Qv8mGAySn58/QRZh0DpI65FWBARCkRChaAitSkvbUBt1fXWEIiH8YT9hIUyqLhWP3sNIaISD3oMYVUY8Rg/9gX4WpyympqcGl86FTCKjxFNCJBrBqDJywHuQ3JQlhKIhQtEgK60r+Lj7GCW6VCxqM9kp2XT6OolEI6zPWMvh5sOY5VaWpi3BO9BGXW8dmSnpBCNBajrrkaXKSNFaqGitJkVnxmZIAQQMah2ZqR4O1R1DLVexfskq9p78RAhv8Qp2VBxgWUYeZp0xYRBKlhZw2ttKKBKhaEkex2pqCIZD5GVm0drjpa27J1aeUyKj+nQTBq2WTJeDKLFZ2zM/eIBbv/I353D3jGW0CykZjIJMJsNut+P1epPCKCiVSlJTU2ltbSUnJ2e+u4NWq8VqtdLS0sLChQvHiBROpl81+t9xOROn04nX652gnjqe0WqqEomEtLQ00SgkGzabDZlMNmFV0NHRMWH1EMfpdOJ2u8d8+Xl5eQiCQHNz8xlvdIfDwebNmxPFR1544QUkEgnPPPPMlNdotVqOHTuGUqmccBMVOYsYCY0QjAQREPB/UufAprWhVWgZCY0AYFQaMalMyGVyRsIjbHBvwKgyMhwaJs+ah1PvpKa3BpfBxc7mnTj1TrxDXnLMi+kP9JNpysSsMnGs4zhEYkZJJpUilco40no0FtqauZ7dp/cBUJixkg+qdhKMBHEZHQSiEU73NLHAlkXvyAAmmQW3xYlUIqG6rY7SBeuxm2yUN1Vh1BjwWB0IRFErVCxNX8i+qjKkEikZaQ7e3h+T6C5dVsCuE0dBgILspRyuOokgCBQszuXk6QZ8gQClq9dwsraRrr5ubBYzJr2O8po6VixcxKtbHuPaK4qn/b5mQ1paGuXl5eTm5ibFj97pdFJeXs7ixYuToj9ut5sTJ06wcOHC86r7NB1xkcKpJMfr6+tpamqaVKRw9CRttJaVSqVCIpEkrmlsbGT58uXT9mG+ZUfOJ59Ko6BUKiksLGT79u186UtfShzfvn0711133aTXlJSU8Ic//IGhoSH0ej0A1dXVSKXSsyqavmnTJjZt2pT4u729nR/84AfTXmM0GgmFQvh8vgkyCjqljixTFm3DbUiQIKgEQtEQkWgkFpqqMhGKhpAgYTA0SEtPC82DzWSbsxEQ2NOyB5vGhlKmJCpEsWpiG6S5KbmkG9OxqVMZCg7ROthMeWcsfPYy9yZau1v56PRO0rQOPEY3OrmeXn8/AKVZxXSPdBOMBFmbUUhZy3GKXIVoFBoaOpsYDAyxMiefIw0n6B7qJSPFTY+vl9r206SZbGhVGiqaT7E2q4Bsh4cjdRUJ41DRUh0Tv1uyImEQSpatpq9zEEEQWLdsOYcqK4hEIyxfuAiZTEJXXz8ZDjvhSJTaphbMBj0/++4DbFg19Q/4XIi7kPr7+zGbzRfkNWbaHyBplFOtVisSiYTu7u5JS86eLYIgEAqFzmpWH888jg/m46XHa2trycjIwOl0olQqZ2SsJBIJTqeTw4cPs3jxYlQq1YQ20Wg0sbL4tPCpNAoADz30EDfffDNFRUUUFxfz7LPP0tjYyL333gvAI488QktLC7/97W8BuOmmm/jnf/5nbrvtNn74wx/S1dXFd77zHW6//fZZFRIpLS2loqKC3t7eSTWOIOYCMJlM9Pb2Tqqt4zTEZvkRIUJYCCNFSo+vBwCNQoMECYFIgM6RTrpHulmSsoR0YzrBaJAN7g2YVWb6An0UOgqJClFUMhUj4REOtB5ghX1FIiku35aPTqklQoSa4VqQwGpXATtqd9EcauWy9I0UuFayq2EvBqUhUYkNQKtSc7DuY0KRECs9y+gc6aJ7qJclzkW093fS2NPC+py1NHQ2U9/RRJoplYHAILWtrZi0elzWNI7UVaCUKShZVsiu8iOAhA1LV7H7xFEW2DwU5uSy/5PiO2uWLOXjmlO4bX5yszLo7OmjZ2AAZ6qVP//iJyxbeH7rGI9GKpWSmppKe3t7UhiFuHKq1+tNCqMQr3nc0tIyqVGIRqNnNdDHXTjxMqGj99rGlwk9U0GhcDhMV1fXrOpby2SyhHGJq6dO9p7ibT8tfGqNwg033EB3dzdPPPEEXq+X/Px83nrrrUSBb6/XOyZnQa/Xs337dr75zW9SVFSE1Wrl+uuv51/+5V9m9fp2u52cnBz279/P3/zN1L7teL6C2+2ecK7IUcS+5n2oJWoEiQACmNVmwpEwvrCPkXDMvSSRSHAb3ZjVZnr8PRxuO0yqJpWFKQvZ17KP5anLOdZxDJlERk1PDUppTB5hY3opLYOtKOVK9rceINOYQaYhE5kgpWuki5HQCEtsuQSiAY62foxKpiIvLZee4Vi8fmn2evac3hfbOM4q5HDjx4SjEdYvXMfHTSfwBf3kOXNQKRW09XWSnZrOSNDHSW8NJYvX09rTQWVTLUaNnvRUJ4IkikImZ9XCJeypKAPAajFRWR37njYsX8He8uMIgoBBr2G4O0zPwAC5WRn8acuPyXBO7ho8n6SlpVFRUZE0Lpu4cuqFrBA3HeOrxykUCjo7O6msrEzUio4/wuEwwAT3jUqlwmAwTDh+Pt6Py+WitrZ2jAfgbIl/vx6Ph6qqKrKzsyesNCZTU02G++JckAjJENP2KeX2228nJSWFJ554Yso23d3dVFZWUlpaOuHcUHCIm/58E4FwAAGBQDiARCJBKVPiC/vwhXyJFYBeqScqRKnoqsAf9rPOtS5WqCcaIU2fRn+gH61CS21vLXKJnOrealamruLj9o8p8ZTQNtSOVZNCU08L3uE2zCoz+dYV7G3cRyQaYYkljwgRTnXVUppeSjgcYd/pWB3mqxdcxbsVHwKwPrsIISRlf+1RVmcup7L1FFkpGUjCMlp62+kfGSQ7NZ3slEw+KDuA3WRFr9ZS197Eiow8hICM4/WnkEmlFC3OZ//JY+SmZGO1WNlTHlNGXbs0nyNVlaxbVEDQH+GPP38S6zQbgeeTaDTKjh07KCgoSIrVgiAI7Nmzh4ULF55X5VRBECadzU92bHz1uLiqrM1mmzCrn2z/7EJTXl6OXC6fcSIqxFYa0WiUAwcOsHjx4gmRSCMjI+zcuZOrr746cUwul1/UK4dP7UohGdi4cSPPP//8tG1MJhN+v3/S0Dm9Uo9da6dtuI1QOIRWoSUSjaCWxaqvSSSxwFJBEAhGg3SMdCBBQrY5m5AQ4oD3QCwqKTxCZXclJZ4S6vrqKPGUUN1bjVWTQolnA4IQpba3ltreWopdG1AISmQKGT2+HiJChNWuVaikWvae3k+KxoJMJmFX7UGkEinrMosYCg0BULpwHbtq97M2o4j1Cws5UBfLXtaq1bS2d9M/MkieexGtve0EQ6FPJLRD1LU3YTVY8If9tHcMoFGqyE3PZv/JmBEwm/UJg1CyfCW7j8fCVzPcNn7x0MPo5rBOcNyF1NHRkRRGIe739nq9Z2UUIpHIWUfhAAkXzujBfXRN6Pjx0S4cr9dLfX092dnZSTFr9ng8HD16lEWLFs24HoZUKiUajeLxeGhsbJxgFOZrhXYhEY3CBaS0tJR777132ljpeCZkb2/vpPHQS6xL6BjuAAmxmgpIaRlsIUoUjTyWYBMIB2gfbqfH30O6IR2b1kZdbx0AGaYMGgcaWZG6ArVcTamnFI1Cg1PnpHGwkZruWhBiNRfUcg1GlYG9IzF3zWWeyyjJKGZ3417WudeyyLaQ4cAwO+p3kmHOxqI1sbfhAJmmdDYsWMOu2v0AaJRKdlYcJipEKV5YyP66o6zxFOI0p1LRUoM/FMBptiMJKjnd1Eq61UEUgerWejYuWk9nbx9ltSdjuQ0LFvNxfSxjed3S5ew+XgbATVf9DVsffgTFPBS9SUtL4+TJk+Tk5CTFoJeWlkZtbS29vb1Thl7G/x8Oh2OrzXFROCqVaoK/frYuHLvdzsmTJ5NmQ95kMqHRaGhrazuroJHRjFdPHR+eOplRSIZ74lwQjcIFZNGiRZjNZo4cOcKGDRumbBffV5jMKCy3L+ejxo+QSWREhAgRIYJFbWE4NEw4EkYlV2FUGrFqrKjlahQyBYFwAI1Cw5KUJYSjYZoHm7Fr7XzQ8AEmlYlAJEAoEsI77MVj8OAyuLGozLxbt53ukR6kEinZuthqY2/jAQAUMgUtfS34wn48JjfZ5gx21OxGq9Bg0Zk53dOMBAnFC4rYUbOHPMdSrHoLu07FrjfqdXzwccwVtSpzGVWttaxOX8ViVxbdg310D/bFKrMpZZxsqseg0ZKZ5uZQ9QmkEgkrMxcmDMKD19/Ev9x937z9+KxWK+FwmIGBgWnj18+V+AB/Nm4cgMOHD6NWq8cM7Hq9HqvVOqFU6IX87OIx/i0tLUlhFCQSCenp6TQ2NuJ2u2f83mUyGdFoFIfDMSE8VVwpiMyI0UV3pjMKZrOZmpqaSc8Vu4t58eMXCUVCKFESCAUIRoMYVAb8YT/+sB9f2IdarkZAoD8Qq6cQjARZ61pLVXcVEItW0sg1rLKvYiQ8gkVjoWWwBb1cz76W/ax1rgHAqrGw2l7Ah6c/onawDo8xHZfRxa7G3eRalqCWq2nobcQXGSHNYMeg0lPWepyNGaWkGVPZUxfbZ8iyu3n74w8BKM1Zy/66mCbRukUFHKo7RiQaQSaH5u52RgI+FqSlM+Qf5mBtGQ6LDZ1GQ3nDKdRKJXkZCwgOxWLGf/z33+SbX7nxvHw/s2W0C2k2RmH0BuyZonAgVidgvG9eq9WOOdbZ2UlHRwdr16493293VrhcLg4dOkRubu68ljCN43A4qK6untXqJb5acLlcHD58mNzc3EQtC9EoiMyY0tJS3nvvvWnbWCwWhoeHJy2cYlQZ0Sq1dAx1EBbCCAiMhEaQSWRolVo0cg1SiRS5NPZVSpBQkFaAXqmPJYWZMshJyaHP3xeLVooGOeA9QKmn9JNiPMUxyQuJlCJnIYe9R3DrY0vs5an5GJUmdp+OhZ8utGXz9sntCIJAIBKrSVvTVYdVm4JCIeNI9TFUciXLXXmc6oq5rzYsKkqsFjbnX8l7x2ICeWsXrmJ/7VHUMj3LMnJo6vQy4BsiI9WFQ+vkQOVxzDoDTmsqR2tOYjem8MQ37ph3gxDHbrdTXV3NokWLkEgkidj6s/HXx2PrR7tpVCoVarUak8k0wV9/NrH1CoWCmpqaaeuDzyVGoxGtVkt7e/ukkXVzjUwmw+Vy0dTUNKvVy+jw1KampkR4qmgURGbMxo0beeKJJ6ZVW1QoFOj1enp7eyfNuM6z5jHojyVxSaQSDEoDQ6Eh/CE/UaKEo7EQ1bahNgaCA2Sbs3FL3FR2V9Lt66bEU8KJrhOkaFJoGmyKuaKiEda71qOUKTCrzOxv3U9uSm5MVkMIsdSSx/Gu46x3FWPVWPGY3TT0nY4lkqWvoaz1GAuMi9Aq1ATCIXY37MNuSMWqs3Co8WMUUgUlOWvYfSq2cijJWcNwaBiADYuL2FMV0z26fNkKPjx2kEAoSK47m87+HuQmCY4UGyqFksrGOnRqDU/f/Y+kSFTTSpVcCKby0fv9fnw+H3v37k3M/ONJTONn9QaDYcJm7fl24SSbciqQyFlIBqMAsQ3nffv2EQgEJk1Em474d+V2uzl16lQiPFXcUxCZMatWrSIUClFZWcmyZcumbGexWOjr65vUKCxPje0rRKIRgtEgESGCXCJnMDhIb6AXX8hHIBJAJVORa8nFZXAl6iysSF2BSqai2F2MQWGgsqcSp97Jfu9+9Ao9A8EBMg2Z9AZ6yTRlYlKZOew9jEYaS6aTS6VEifCx9xhKqZLLskv4qD4mR5FucbKn/iBDgWHSTW7cugz21cWktdNT3ESFCHKpnNWZy9l96iCZFg8li9ewuyrmSipevJr+kQECoSCrsvOoaqnHF/QzEh4iGo1yur0Vm9HMG49voWBRHjt27Dhvfvy4PMJ0oZaBQCAhdRB34YyPrVer1YmiTPEonPnC6XRSV1eXNFE/cZG82eQIXAh0Oh1ms5nW1tYZJ7PF1VNTUlKQSCR0dHTgcDjElYLIzBlddGc6oxCv8ToZxZ5ith7eilwqRylTIpPIYtXb1GYiQoRQJEQwEiQcDSOXyhkIDnCs4xhSiZRCZyEHvAfwhXysc6+jaaCJYncxzYPNLLEtYTg4TKYxCwlSWodaKe+IlbMsdK6mqbOZXc27WWhYFJPWUJvwhX0xCYqsYhr7WxgKDMcE8vrakRnBYbSjUag50XqStemrWerK4UB9TPzOYUmlwRuTMy7NLWJXVcyArM9dyaGacsKRCEvTF1Hf3kyKJpVMlYs/P/F/yXHHEg6tVitdXV1TGoVzkUeID/QajQaz2TwhCmeyVZ7RaKSmpiZRhGe+SU1NpaKiImmUUxUKBXa7ndbWVhYvXjzf3QFi5TqrqqrIysqa8XcWD0+N16UWjYLIrCkpKWHv3r2Jgj+TYbFYOH78OKFQCIVirPa/SWXCqrXSMdyREMjrD/Qn9hWkxIXsZAyHhqntrSUUDbHSvhJBEHDqnHiMntjGt6cUnULHQvNCFFIFJ7pOoJKpaOhvQC6Rk5uyGIsmhZAQonYkti+wODWHnfV7aB30st69jnXpa9hdvw8EuCx7I/saDhOMBPF9kixX391Iqt7KSGSEk62n0SjULHEuYn/dUUoy15Np87Drk9XC8sxc+vtGCEciFC5YxonGWvyhAFct38iPb38YZ4otIY+g0+lobW1NqMtOFpETl0cY7683Go0TfPXn6sKx2WyUl5czNDSEwWCY9fOcL5JNORViLqTy8nIWLVo0ZyJ502Gz2Th58iSdnZ3Y7fYZXRvfcE5LS6Ouro6BgQHRKMwnl19+OatWrWLLli3z3ZUZs3HjRl566aVp28QjSvr6+ibVjVlgXkDbUBtRIUpUiGLT2ghFQsgkMlRyFRIkhKIhAuEAboObRfJFaJVaPm7/mKHgEA69g13Nu3Dr3fgjfrp93YSiMddIt7+bYvd6BoNDKKVK9rXsw6lz4ta50Mp0tAy1MBQcItuciT8aoKzxk1rIC4oJBIIEI0EKPCs52VGFVZlKtjUdfyhIeetJ1mWtpW9kgKON5ShlCnRaNe8diRUg2rC4kN1Vh1iXuZrC7GUcrTtJVIiyOjOP24s/R/3JaqqC5WNcOKFQiPb2djQaTSLkcvxsf65+pDKZDJvNRkdHR1IYBUg+5dSUlBSkUildXV0zHoQvBHGBy+bm5ln1Jx6eGq/HrFAoxD0FkZmzbt06WlpaaG5unjZ5xmw2T2kU1jrXUtZWRkgIMRwcZjg0jFwip9vXTbevG1/YRygSQqPQ4NA50Cg0dI10MRgcZEnKEvr8fRiVRnKtufQH+lmVtoqh4BBmtZljHcfQyfVUdFZQ4inBoXeQbc6ipdfLqYFTKAYVlGZu4FDLYer7TrPMsQKlTMGu+r2sca2hJHsdexsOEhWilGYsYm/dYQb9QziNDuQSKVVtteiUWhyGVD6oiuU2ZJid7KmObTaHgn6O1MVCcq9Yupaf3vSPGHRjB/u4C+fgwYM4HI4ZJyFdKOKzxsnE0uaDeK2HZFFOHS2SlwxGAWKbxXV1dbMqCDQ+PNXhcIzZtL7YDQJcJOU4b731Vnbs2MEvfvGLmLSDRDKl//1MbN26lezsbNRqNYWFhezcufOsrtu9ezdyuZxVq1bN+DUNBgOrVq06Y4nOeBLbZKx1ryUYDRIIB5BJY7OVUCSEVW1lUcoiVtpjJTfXOteywLwAvVKPQWlgtWM1boObpsEm/GE/Q8EhDrcdxh/2s791P1pFbEM5RW2hwFGAXCqnc7iTPc17cZvcpKns5FhyGA4O4w8HWGhZiEmp52jLx8iQIoTD7Kk/QFSIkmfJob69nkH/EOl6F8P+Yep660nRmLFoTNR2n0YhlbF6wTJOdtYDsdXCkdYK0m0O7tp8PX/6wa/Jy12Cx+MhNTUVo9GIWq1OuB5SU1Pp7Oyc8XdwobDZbPh8PoaGhua7K0BsUIorpyYLLpeL7u5u/H7/fHcFiK3K7XY7zc3Ns7p+dHjq4OBgUuRhnE8uCqPwi1/8guLiYu666y68Xi9er5f09PQZP89rr73Ggw8+yGOPPcbRo0fZuHEj11xzzRi11Mno7+/nG9/4BldeeeVs30JiX2E6LBZLwk854ZzaQoYpA5PShFFhxKKxIJVIGQmPwCeShqFoiMHgIE2DTexs2smRtiMAdPm66A/0s8S2hJre2Iw8Eo2wInUFZqWZVfZV9Pv7Odp2lB2nd2BWmjEpjAj+KF3+Hiq6KvEP+1lqzON0XwPtg+2YlEayzVkc6jjKAksmaz2rqew9xemRJtZmrqYr0MNAcBCVWoXDYqe530uKzkyGzU1EGkEhk7Nm4YrYakEC37zu6/z8zkfP6Pqx2Wz09PRM+hnNB3K5POFCShacTicdHR1J8xlpNBpSUlKSylClp6fT2to6q89odHjq8PDwp2J1MJqLwijEE3q0Wi0OhwOHwzErv/HTTz/NHXfcwZ133kleXh5btmwhPT2dbdu2TXvdPffcw0033URx8eyreV122WVnNApxiYK+vr5Jz6dp0xgKDTEQHGAwMIhMKmMkPJLQPerx99Ax0sFQcIgsQxalrlJS5CmoBBWrrasxYkQlUZGpyaSsrYzyznJ2N+6mrKOME90n0Eg1pOvSWWpeij8U4GhvGRIkONRpmM0mKgYqCQsRtDoNJq2Jmr46VDIVOc4FHGiOGaCijAJCQghfyM9yVx49w72YdUY8Fic6lZaqtlpaB7wscS3kYG0sQuqXt/2Q+//m5rP6cel0OlQqFT09PTP+Di4Udrv9rAq8zxXxvIhkWlG53W5aWlpIFlFms9mMWq2esmb7dIwOT4WYUuqniYvCKJwPgsEghw8fZvPmzWOOb968eVq3zosvvkhtbS3/9E//dE6vX1JSQnl5+ZQDPsRmIPF9hclYlbYKlVSFTqZDJ9GhiCqwK+xYpBaCviDt/e009jXSNdjFyMgI3f3dVHZVcqDzAAOBAVpHWvH6vNgNdvxRP7kpuUhksYikYk8xazxraBppIiDzE4gGUcqUXJ69ic5AF3ub9+ExuinN3EBFZyU2vRWHIY1MSzoNfadj73HBOvbUH0CjVLE2azUn22sY8A8ilQv4gn6aelpJNViRS+X4Qn7UChWvfuv/cttnrj/rz1EikSSdCyk1NZXh4WGGh4fnuyvAWOXUZCE1NZVwODyle3SukUgkeDwempqaZmWo4u5MpVI5ZoLyaVg1fLqcYdPQ1dVFJBKZkByWlpY25Wzh1KlTfP/732fnzp3n7Dd0OBwsXLiQ/fv3j9FejxcpiYdXSqVSvF7vpMlVIX+I9u52okRjNWQJIZPGoo/06tjGrFPiRC1Xo1Ko6Pf34xvysdS2lAxjBv2BfjwWD2qZmhX2FVg1Vip7KhEQ2N28mw3umD5T50gnpeklHOs4jj/iIyJEcBtcLLEt5n9q/x8AVp2Z+u4GqgfbMSj1rM8sYnddTCVVrVTyQU3M0K7yLOdE60l8wTBZ1nQCwSC1HQ1cteRyfn3nUxQvXj3jzzIeCjrX2c1TIZfLsVqtdHR0zKrC14XA4XBQV1c3qXTKfCCVSnE6nbS2tiZm2PNNPLluNgmR8Q1nuVzOyMgIAwMDSRMGfK5cNEZBqVSeFx/p+EFkqoElEolw00038cMf/nDWiTeDg4NUV1cn9kH0ej0///nP2bJlC2vWrOGqq65KyCPEi5TI5XJ8Ph/RaDThBhgdX/+Xd/5Cl68LAIVUQVSIIpPKEtpHUSEme9Ef6Ke+v55QJIROoaNxoJGKrgoKHYUcbjuML+Qjz5YHwEhoBLvWjlqmZrWjgI/bj6GQqBgIDNDt62K1rYDjPeU4/E4kSCjJLOZkdxW9vj7STW7kMjlRosgkMtZmruaDmo/ITMnCZXJyoOEokWiEK3Iu53DdcfpHBvCkOPnR//c98lw5s/pcLRYL0Wg0aZK0IDa5aGxsTBqjoNVqMRqNtLe3z2r/7ULgcrk4cOAAubm5E3Jx5gO5XJ7QQ5ouIXL0pG0yqROLxcLp06fHqKdezFw0RiErK4v9+/fT0NCAXq9PxD+fLTabDZlMNmFV0NHRMam0xODgIIcOHeLo0aM88MADwP8W6ZbL5bz33ntcccUV077mhx9+yO23347T6cThcKDRaPD7/Vx55ZWsXbuW/Pz8xIAfX4kIgsCOHTtwOp2TCncttCykY7iDiBDBH/Yjk8roGewhEAmglMdmhMOhYdqG2pBJZORac1FIFVT3VGNWmjEqjWSbsknTpRGIBljvWh/bk/D18EHjBzg0TiJCBLvOTqrWRlVXNZFwJ6FoiIHgAEvteew6HVsFXLZgE2UtxxgIDOLwOFnqXMLehpjW0VJXLm8f/wCAosxVBMNB+kcGWOpezJ++9QLulIky4WeLVCrFarXS2dmZNEYhnk0crzqWDMRdSMliFAwGA3q9nvb29nkPKY5nv8eTRg0Gw4QCRHEDEI1GJ9W0MplMpKSkoNVqKSsrIzc3d8q6KRcTF41RePjhh7nllltYunQpPp+P+vp6srKyzvp6pVJJYWEh27dv50tf+lLi+Pbt27nuuusmtDcajRw/fnzMsa1bt/LBBx/w+uuvn9WM8POf//wY33dVVRUrV67k3XffnVKQSyKRJEJTJzMKK+wrOOA9gCQqIRqJEgwHsWqthCKhxIrDprGRY85BJpMhlUjpHO5Ep9CRZcri9MBp6vrqMKvN7GreRUFaAfX99eTb8invKme5PZ8FoQX4Iz4ONcfyCNa7ihnsG6Smv4Ycy2KkSCnOWE8kEmEgMEi2JZP+YD8VradQSBUUpK+gZbAVgJKFa9lTdxCnwUHp4rW8dv+vMWvPfSC32Ww0NjYmTX6AQqFIuJBmcl9eSNLS0qiqqkoqQxXfcL5QRmG0gOFkA/zof8cneBKJJLFaiFeWG28ApnIfx8t1ms1mmpubycmZ3eo3mbhojMLixYvPGL1zJh566CFuvvlmioqKKC4u5tlnn6WxsZF7770XgEceeYSWlhZ++9vfIpVKyc/PH3O93W5HrVZPOD6T92AwGDh69Cjr16+fsp3FYqGrq2tSw1OSXsLvTvyOcDQck7UIDuMP+1HL1bGM5kggVkRHFkIeldPr76WiqwK71o5OqaOsowyrxkqfvw+XwYVdZ6fEU4JRaaR5sJn+YD8HWg4il8jRKXTk2/NRy1TsG4ztF6TqUllsi7D79F4KHKso8hRQ2VHNcHCY1emF+EN+Dpw+HBPPW7Sej2r2AVC8sJBnb/4ZasX5mUnZbDYqKiqmrWo318Rj35PFKMSVU9va2pJGOTVuqAYHB2eUBR6XOplssB+/9waTCxhOlf3e1tZGTU0N+fn556SHdOrUqaSZpJwLF41ROB/ccMMNdHd388QTT+D1esnPz+ett94iMzMmuOb1es+Ys3AuSCQSSkpK2LNnzxmNQk1NzaRy26naVFRyFcO+YcJCGIVMgS/gIxgJolPq0Mq1yCVyZFIZAgImlYmNno3oVXr8YT9LbUuxaWwc9B5EEARqemuo7a0lz5pHX6CPU72nsGls5NpyESKwp2kvVo0NGTKWp+TTPtLOyc5qZBIZeqWOAw1HCUQCLLRmY9IYONL0MSqZiuXupQwHY6F637riLp687tHzqn2jVCoxmUx0dXXNuysijt1up7KyMmlqGkDMhVRbW5s0yqkKhYK0tDRaW1vJzc2dsuDQ+GNxqZPxJURHlxGdaQ2KOHa7naqqKrq7u7HZbDN6P+PDU5NpD2e2SIRkCRy+RHj66ad5//33+cMf/jBlG0EQ+PDDDyksLJzUZ/6j3T+irK2MKFGET/4bCg4xEBggLIQJR8MMBgZpG25DK9eSk5KDWq5mf+t+jCojS21L2duyl1X2VZR1lOHRe0jRpmBWmen2dRMMhzjVc4oN7hL2NO5ltbMAISThaHsZCLDUmk9UiHCys5qVqatQyZQcb6sg25xJe18PNp2Vqo5TlGQU86WV1/L3m267IJ9lfX09fX19FBQUXJDnnw1HjhzBarUmJhrzTSQSYceOHRQVFc3Z/osgCGMG+/ED/PDwMIODg8hksgkFh8bP5Ec/FArFBRPVq62tZWBgYFb3UjQaJRwO09LSQm9vL6WlpRegh3PHJbVSSAZKS0t58sknpy26E89X6O3tnfSHnGvLZU/LHsLRMMFIrL6CUqYkQoQ+fx9DoSEQwKV3kaZLw6QyMRgcZKV9JWn6NEKREOvd6zEpTaTp0nAZXBzwHqDQUciJrhOUuEup661DKVOQa83liPcoJZ4SANa51yJBxr7GA8gkMtwmJ29VxirLRYQIZo2Jqo5TaBUa/uGKu/lc/tUT+n++SE1Npa6uLqmUKuNS0cliFM6ncupkkThTzfDj9/f4AT4eJFJTU0NGRgZut/uC14w+G9xuN/X19bNa5cXDUx0Ox0W/SgDRKMw5BQUF+Hw+qqqqyMvLm7JdfLN5ssGl1FPKi2UvIpfJUcliG9ZyiRyzykyGIYNQNEQkGiEqRIkIEVqGWqjuqcaj96BVaNnTsgeXwYVeoad9uJ0F5pi/WSPTUGAvQK/QYVKZ+PD0h6RpYlFCMomMTH0G+1sPsM61DrfRhUFloLKrEoC16UUc95azPHUFw8ERXr/9ZQo8K873xzeG0dnNk4kIzgd2u52TJ08m1V5HXDk1Jydn0omIIAiJmtDTDfjTReLEXTjjN2enGuyDwSC9vb1JE8KrVqtJTU2d9WaxTCZDEISkyAk5V0SjMMcoFIpE0Z0zGYWGhoZJ8yjsOjsmtYkefw+BaAAJEvoD/QDolDpkktisORwN0+Proaa3BqPSSLopnbahNpx6J8usyxgIDrApfRMCAgtMC2gZaqG+tyFhaJDAcns+br+bfS37kERjz6uSK+j3D9Ay0IoUKZcvvIwPa2PCgm6Lg1e+8Rwu0+xDTs+W0dnNyWIUlEolFouFjo4OMjIy5rUv8UgcuVxONBqluroahUIxbR2K8S6cmUTizIT4Xkcy7b94PB7KysrIyMg4Y7nOuNc9GAzS3t6O1+ultbWVaDTKzTffPBfdvWCIRmEeiIvj3X777VO2icdNDw8PT1rKMNucTW9bLwgQFsKYVCaC4SBEYwOTDBlhaRirxkqKOgWNQkM4Gqauvw6bxhaLMmo9wBrHGg62HcSj99A81EyaNo0oAqsdBTT0n2Yg1M8Rb0zXaKP7Mpq6mviocRc5ptyE9HYgEgDgKyu+xLYv/xytcu7CH202GydOnEia7GaIrRba2toumFEYHYkzXejl6EiceAlJq9WKUqkcE4kTH/Tn0gWnVquxWq20trYmTcROSkoKTzzxBDfeeCO33XYbXq+Xtra2xP/jg//of3d3dycmJ06nkxUrVohGQWTmbNy4kf/4j/+Yto1UKk3sK0xmFIqcRZzsOklYGmYkNEIgEkAhVzDgH6BpsImh0BASJJhUJlK1qYSiIU52nwRiCXBxtVS1Qk2eNY8sUxYZpgzUMjUfNPw/hkLDVHVXYVGbcRtcZJgyEIjSMBLTOVpkW8Cuhj14B9tY4yriqWse51ulfz/nA7PFYiESiSRVdnM8mmWmLqTxm7NTuXNmE4kzMDDAoUOHWLJkSdLsv7jdbqqqqliwYMEFv2/iM3ufz5dQGBg/4McTW5966ikefvjhxH6Mw+HA6XTidDrJyspiw4YNib/dbjdpaWlJsS9yvhCNwjywfv16mpqaaGlpwe12T9kuvq8w2ebVOtc6ni97nlA0hCARYq4CIYhZbUav1BMRIqhlatRyNQqpgmA0yBLrElQyFXKpHIPSgE1r43T/aRoHGtEr9Rz0HmSdcx0AbYNtLE9djkauod83yN7mfWSbsrCpbdg1qTQPNjEYGMJldPLk3zxOSebsFWTPhWTMbo4nQHV2duLxeAiHw2flrw+Hw4m60aMH/NF1o0cP9jMZhAwGA2q1ms7OThwOxwV892ePzWajsrLynAoCxQf7oaGhCQN9/BEf8Nva2ujv70cul5OWlpZQGnA6neTk5HDZZZdhNBq54447eOedd7jiiium3Rf5tCIahXnAaDSycuVK9u7dy1e+8pUp28WzJCdzjTj0Dpw6J32BPgAEpcBIeIRgJIhcKkcqSIkIEfoCfXT5uqjvqydFk0JeSh6V/ZV4h7yUeErY3b2bNF0aNT01ePQelHIl613rqe2rpdffR4+vhxJPCS0DelxGFw3BRip6K5FJZHx1+Zf52d/+BKt2fgXO5iO7OS6TMNVg7/f7qa6uprq6etpInLg7Z3TY5YUYhEYX30kWoxDf9H722Wd55JFHxpwTBAFBEBgcHKS1tXWM62b8o729ncHBQZRKZUJaPz7gL1u2jKuuuipxzO12JyRvpvqcP/zwQ15//fUxwpWXEqJRmCdKS0vPaBRMJhPBYBCfzzepTEGqLpWWoRZCkRARIYJMKqPX38tQaAiFRIGAQH+gnx5/Dw6tgxxrDgqZAo/Bk1g1rHGuwag0sqdlDzatjZ1NO1lgXEjnSCdrnetokDSgV+iRSaXsbtrDeud6Bv1D/GTzU9y8+mtJMYs6n9nNoyNx/H7/hNn86MFfEIQpI3HMZjNVVVUUFhZiMBiSYsbpdDrnXTk1Ptj39fXR1tZGQ0MDP/nJT4BYCdH4QO/1emlvb2dkZAS1Wp0Y5OOD+6pVq3A4HLjd7oQrx2q1JsJDz4XvfOc7SVU0aa4RjcI8sXHjRp588slp28hkMkwmE729vZMaheWpyznefhyZXBaLOJKASWUiEo0QiAQYCY2gV+hx6p1oFVoi0Qgft3/MQHCAYncxh7yHGAoOsda1Fl/Yh11n51TvKbLMmTh0aRiURg75uni/4X0UEgUyiYzLsjfyyOLvsSQtd94HuThnk908WhNnOn/92UTijDYC00XixAe1ZJGK1mg0mEymC5J1Gx/se3p6pnTjjHbl+P1+tFotTqcTo9HIf//3f1NaWkphYSEulwuXy4XT6cTlcmE2m8/LYH+25OTkfCo0jGaLaBTmiZKSEo4fP05/f/+0Wu4Wi4W+vr5J9x4uy7iMV068QigaIipE8YV8SJCgUWiICBEEBDQKDQqZAkEQaBpsYiA4wOKUxUSFKCaliQJ7ARKphBJ3CWqZGrvWTm+gl6Peslgk0ifS3PcU3c1tq25lUcoiamtr6enpSQp5iXgkjk6nS7japhrsYawmTnxwv1CROPGKbMnwOcVxOBy0tLSctVEQhNh+VVdX14SBfvwmbXt7O8FgEIPBMMaF43Q6KS4uTrhv4oO90WhEIpHw4osv8swzz/DMM89c4HcvcjaIRmGecLlcZGVlceDAAa666qop25nNZk6ePDn5cxhcGJQG+gP9RIUoWoWW4eAw4UgYg8qAXBpzWQhCbL8hRZ2CTWPDqDRS3lVOt6+bLHMWuxp3kWXKom2ojYgQYTA4iFwqx2Fw8O313+areV/Fof9feXGr1ZqoWHWhZm/TySSMfoTDYSA22IdCITo7O1Gr1ajV6nPWxDlX7HY7p06dSppCNxCbZGzcuJG//vWv5Obm0tnZOelAP3pm397eTjgcxmw2k5aWhsPhwOVy4XA4yM3NTQzy8Uc8Wu5s742vfvWrPPnkk7S1tSXNfselzCVvFLZu3cq//uu/4vV6WbZsGVu2bGHjxo2Ttn3jjTfYtm0bZWVlBAIBli1bxuOPPz7rDan4vsKZjILf75/SX55ny+Pj9o+RhqUEI0E0Sg09vh5ahlqQSqSJfYX+QD9p2jSyzFn0B/vp9nWTbc5mIDgAQG5KLh6Dhw2eDeRac9mYvhG3YfLIKKPRiCAIM65YNVomYTpZ40AgkNDEGe+v12q1k0biAOzevZv09PSkSWTTaDQYjUY6OjrmbLUQ/4zjs/fxA357eztms5nrr7+exsZGotEoFotlzKze6XSybNmyCYN93IV5vicCBoOBmpqapHFHXupc0kbhtdde48EHH2Tr1q2UlJTwm9/8hmuuuYaKiopJE48++ugjrrrqKp566inMZjMvvvgin//859m/f/+shLRKS0vPmK8gl8sxGAz09vbidE7MEl5kWcT+lv1EhAhhIUwkGsGqsaKUKun19xKOhkk3pLPBswGP3oNVa0Uj13D3qrvxGD04dU4yTBnolRNzIaYirgrZ09ODyWRKROKcSelyvCbOeFnjc43EsdlsSZXdDLHVwrkahdHZs6Nn8VP57Ds7OxEEAZvNNmagdzgcFBQU0NDQwBtvvEF1dTUulysx2ZjPQVk0CMnDJa2Sum7dOlavXs22bdsSx/Ly8vjiF7/Ij370o7N6jmXLlnHDDTfwgx/8YMavX1lZyerVq/F6vdO6F6qqqohGo5PKYrQOtvKrw7/CoDJgVplJUaeQqkslVZNKmj6NFHUKMuns/OPxSJzJBve+vj58Pl9CNmF0JM5UKpejN2cvxCDQ3d3NiRMn2LhxY9IMMiMjI/zrv/4r99133wRjFf/pBQKBWWXPjh7w44/4rN7hcCSkGsZ/Fj6fj7S0ND744AOKiorm5oMQuWi4ZFcKwWCQw4cP8/3vf3/M8c2bN7Nnz56zeo54neDZRpcsWbIEnU5HWVkZa9eunbJdvL7CZLgMLp68fPoopvGMj8SZaoYfCoWmjMRJTU2lvr6eFStWoNFozpsmzrmQLNnN8cF+ZGQEr9fLG2+8QX9/P9nZ2ROSqdra2ujt7Z3T7FmNRsOzzz4749oBIpcGl6xR6OrqIhKJTKjPnJaWNqGO81T87Gc/Y3h4mOuvv35WfRhddGc6o2A2mxkeHj7jhuVUNWYnG+xhYiTO+OpUZ4rEaWtrQxAEdDrdrN7/+eZCZzdPlz0b99fHZ/Xt7e2J7FmXy8Xrr79OcXExLpcrkT07OuzSbrfPaS7DjTfeOCevI3LxcckahTjjf4RnG1Hz6quv8vjjj/PnP/8Zu90+69ffuHEjO3bs4MEHH5yyjVQqRavV0tzcjFarPWMkznjXzYWKxInvKySTD3822c0XOnu2vr6e/Px8/vM//3NGG/MiIvPBJWsU4qnu41cFHR0dE1YP43nttde44447+MMf/sBnP/vZWb2+IAj09/fj8Xg4duwY27Zto62tjRtvvHGCfEIkEgGgoaEBvV6fGPSnisSZq9mm1WqltrZ2Tl7rbDGZTNx333388Y9/JCsra0z2bFwIbfRsfi6yZ3Nycli2bBk7d+7k2muvnYNPQURk9lyyRkGpVFJYWMj27dv50pe+lDi+fft2rrvuuimve/XVV7n99tt59dVX+dznPjer1169ejWVlZX4/f6Elvy///u/k5aWxhe/+MVJM2e7u7s5ffr0tG6muSYlJYVjx47NeUGZM2XPhkIhbrvtNjo7Oydkz46e2RcVFU0IuzSZTBcke3bXrl2TZqWLiCQbl6xRAHjooYe4+eabKSoqori4mGeffZbGxkbuvfdeAB555BFaWlr47W9/C8QMwje+8Q1+8YtfsH79+sQqIy4fcLZs3boVk8mE0+nEZDLxmc98huuvv55bb711ymssFgvl5eWEQiEUCsXs3/R5RKFQYDKZ6OnpweVynfPzna/s2cWLF9PW1sbzzz8/IXt2vqKSRIMgcrFwSRuFG264ge7ubp544gm8Xi/5+fm89dZbiRKYXq+XxsbGRPvf/OY3hMNh7r//fu6///7E8VtuuYWXXnrprF93/fr1Y/6ObzZPZxTUajUajYb+/v6kihrRarXs27ePL3/5y1O2iRdyH509O1WM/fjs2dEx9mebPXvixAnWrFnDhg0bkqaql4jIxcIlnaeQLLzzzjvcd999lJeXT9vuxIkTKJXKpBHrEgSBv/71r9xzzz288cYbdHR0TMiejf/d0dExZfZsfKAfPeCfS/asIAg89NBDfO973xNlE0REZohoFJKA/v5+UlJSqK6unjRrOU5rayvNzc0XdF9hptmzPT09AAl32OiZfXygHy2ElgzZsyIiIlNzSbuPkgWTycSKFSvYu3fvtG4Yi8VCRUUFkUhkxiqeZ5s9G3/Es2fjCVXxQd7j8bBmzZoxM/v777+fTZs28Z3vfEcc7EVELnJEo5AkxPcVpjMKarWav/zlL0ilUq644gpgYvbsVBuzFzJ79uqrr+a///u/+e53v3v+PhAREZF5QXQfJQmvvfYaP/nJT9i1axcwdfbsc889h8FgwGw2T5o9G5/Vj5Y3Hu+zP9/Zs93d3fT397NgwYLz8nwiIiLzh2gUkoSmpiYyMzP5whe+QHd3d2JmPzQ0NCZ7NhwO09bWxr333jvGd+9yuc5Ye1ZERETkTIhGIYlYt24dn/nMZ8jJyZkyezaurNrX15dQwRQRERE5X4hG4SJDEATWr1/PK6+8wqJFi+a7OyIiIp8yRKMgIiIiIpJg7grWioiIiCQJLS0tfP3rX8dqtaLValm1ahWHDx9OnBcEgccffxyXy4VGo+Hyyy/nxIkTY54jEAjwzW9+E5vNhk6n4wtf+ALNzc1z/VbOO6JREBERuaTo7e2lpKQEhULB22+/TUVFBT/72c8wm82JNj/96U95+umn+eUvf8nBgwdxOBxcddVVDA4OJto8+OCDvPnmm/z+979n165dDA0Nce211yZUjS9aBBEREZFLiO9973tCaWnplOej0ajgcDiEH//4x4ljfr9fMJlMwq9//WtBEAShr69PUCgUwu9///tEm5aWFkEqlQrvvPPOhev8HCCuFERERC4p/vKXv1BUVMRXv/pV7HY7BQUFPPfcc4nz9fX1tLW1sXnz5sQxlUrFpk2bEqV6Dx8+TCgUGtPG5XKRn59/1uV8kxXRKIiIiFxQHn/88YRsefwxWqhQmGP/fV1dHdu2bSMnJ4d3332Xe++9l29961sJify4JP50pXrb2tpQKpVYLJYp21ysiEZhCrZu3Up2djZqtZrCwkJ27tw5bfsdO3ZQWFiIWq1mwYIF/PrXv56jnoqIJD/Lli1LVL7zer0cP348cW6u/ffRaJTVq1fz1FNPUVBQwD333MNdd93Ftm3bxrSbTanes2mT7IhGYRJee+01HnzwQR577DGOHj3Kxo0bueaaa8bUVhhNfX09f/u3f8vGjRs5evQojz76KN/61rf44x//OMc9FxFJTsZLsMTreguCwJYtW3jsscf48pe/TH5+Pi+//DIjIyP87ne/A2Iqwi+88AI/+9nP+OxnP0tBQQH/+Z//yfHjx/mf//mfGffF6XSydOnSMcfy8vISv+/4Kma6Ur0Oh4NgMEhvb++UbS5WRKMwCU8//TR33HEHd955J3l5eWzZsoX09PQJM4k4v/71r8nIyGDLli3k5eVx5513cvvtt/Nv//Zvc9xzEZHk5NSpU7hcLrKzs7nxxhupq6sD5sd/X1JSQlVV1Zhj1dXVieJa2dnZOBwOtm/fnjgfDAbZsWMHGzZsAKCwsBCFQjGmjdfrpby8PNHmYkU0CuMIBoMcPnx4zA0IsHnz5ilvwL17905of/XVV3Po0CFCodAF66uIyNnwox/9CIlEwoMPPpg4Npd+/HXr1vHb3/6Wd999l+eee462tjY2bNiQ0PiCufXff/vb32bfvn089dRT1NTU8Lvf/Y5nn302UU0x/lk99dRTvPnmm5SXl3Prrbei1Wq56aabgJjc/R133ME//uM/8v7773P06FG+/vWvs3z5cj772c/OuE/JhGgUxtHV1UUkEpn2Jh1PW1vbpO3D4TBdXV0XrK8iImfi4MGDPPvss6xYsWLM8bn0419zzTX83d/9XWLA/Otf/wrAyy+/nGgzl/77NWvW8Oabb/Lqq6+Sn5/PP//zP7Nlyxa+9rWvJdp897vf5cEHH+S+++6jqKiIlpYW3nvvPQwGQ6LNz3/+c774xS9y/fXXU1JSglar5b/+679mXOsk2RCNwhTM9CadrP1kx0VE5oqhoSG+9rWv8dxzz42ZZc+HH380Op2O5cuXc+rUqXnz31977bUcP34cv99PZWUld91115jzEomExx9/HK/Xi9/vZ8eOHeTn549po1areeaZZ+ju7mZkZIT/+q//Ij09fVb9SSZEozCOuPz0dDfpeBwOx6Tt5XI5Vqv1gvVVJDnYtm0bK1aswGg0YjQaKS4u5u23306cn+uQyzj3338/n/vc5ya4M+Y7Dj8QCFBZWYnT6bzk/ffJiGgUxqFUKiksLBxzAwJs3759yhuwuLh4Qvv33nuPoqIiFArFBeurSHLg8Xj48Y9/zKFDhzh06BBXXHEF1113XWLgnw/JhN///vccOXKEH/3oRxPOzbUf/+GHH2bHjh3U19ezf/9+vvKVrzAwMMAtt9xyyfvvk5J5yqROan7/+98LCoVCeOGFF4SKigrhwQcfFHQ6ndDQ0CAIgiB8//vfF26++eZE+7q6OkGr1Qrf/va3hYqKCuGFF14QFAqF8Prrr8/XWxCZZywWi/D888/Pi2RCY2OjYLfbhbKyssSxTZs2Cf/wD/8gCIIg7N69WwCE1tbWMdfdeeedwtVXXy0IgiC88sorglKpnPDcn/3sZ4V77rlnRv254YYbBKfTKSgUCsHlcglf/vKXhRMnTiTOR6NR4Z/+6Z8Eh8MhqFQq4bLLLhOOHz8+5jl8Pp/wwAMPCCkpKYJGoxGuvfZaobGxcUb9EDk7RKMwBb/61a+EzMxMQalUCqtXrxZ27NiROHfLLbcImzZtGtP+ww8/FAoKCgSlUilkZWUJ27Ztm+MeiyQD4XBYePXVVwWlUimcOHFCqK2tFQDhyJEjY9p94QtfEL7xjW8IgiAI77//vgAIPT09Y9qsWLFC+MEPfjDjPrz55psCIMhkssQDECQSiSCTyYSampo575PIxYNoFEQuOp566imhqKhI0Ov1QmpqqnDdddcJJ0+eHNMmPvt0Op2CWq0WNm3aJJSXl49p4/f7hQceeECwWq2CVqsVPv/5zwtNTU2z6tOxY8cEnU4nyGQywWQyCX/9618FQfjfWXlLS8uY9nfddZewefNmQRCmnpVfddVVwt133z3jvgwMDAjHjx8f8ygqKhK+/vWvC8ePH0+sXn7yk58krgkEApOuXl577bVEm9bW1k+F4JvI9Ih7CiIXHTt27OD+++9n3759bN++nXA4zObNmxkeHk60mWs/fm5uLmVlZezbt4+///u/55ZbbqGioiJxfi5DLg0GA/n5+WMeOp0Oq9VKfn6+6McXmZ75tkoiIudKR0eHACRcfMkgfXzllVcKd99997y4jyZj9J6CIIh+fJGpEY2CyEXPqVOnBCAxqCXDQHzFFVcIt9xyi+iqEbnoEN1HImfko48+4vOf/zwulwuJRMKf/vSnMeeFeSxdKAgCDz30EKWlpYnkorkOuXz00UfZuXMnDQ0NHD9+nMcee4wPP/yQr33ta6KrRuSiQzQKImdkeHiYlStX8stf/nLS8/NZuvCBBx7g2LFjvPrqqxPOzZUfv729nZtvvpnc3FyuvPJK9u/fzzvvvMNVV10FXNqSCSIXIfO7UBG52ACEN998M/H3fPrvH3jgAcHj8Qh1dXVjjieD+0hE5GJFXClcxMy0ENCFYD4kEwRB4IEHHuCNN97ggw8+IDs7e8x5UTpBRGT2yOe7AyKzI14IaOvWrZSUlPCb3/yGa665hoqKCjIyMuasH9P570+fPp1ocz6lj++//35+97vf8ec//xmDwZB4DpPJhEajGePHz8nJIScnh6eeempKP77VaiUlJYWHH35Y9OOLXPKIRuEiZXQhIIAtW7bw7rvvsm3btkn1bi40cxmHHy92dPnll485/uKLL3LrrbcCMT++z+fjvvvuo7e3l3Xr1k3qx5fL5Vx//fX4fD6uvPJKXnrpJdGPL3JJIxqFi5B4IaDvf//7Y45PVwjoQjFa+tjpdCaOTyV9PHq10NHRMStXjfCJLPl0xKWPH3/88SnbxKWPn3nmmRn3QUTk04q4p3ARMptCQBcK0X8vIvLpQlwpXMTMxmUzG4aGhqipqUn8XV9fT1lZGSkpKWRkZIj+exGRTxGiUbgImU0hoHPh0KFDfOYzn0n8/dBDDwFwyy238NJLL4n+exGRTxES4WwctCJJx7p16ygsLGTr1q2JY0uXLuW6666bl41mERGRTwfiSuEi5aGHHuLmm2+mqKiI4uJinn32WRobG7n33nvnu2siIiIXMaJRuEi54YYb6O7u5oknnsDr9ZKfn89bb71FZmbmfHdNRETkIkZ0H4mIJAkdHR38n//zf3j77bdpb2/HYrGwcuVKHn/8cYqLi+e7eyKXCOJKQUQkSfi7v/s7QqEQL7/8MgsWLKC9vZ3333+fnp6e+e6ayCWEuFIQEUkC+vr6sFgsfPjhh2zatGm+uyNyCSMmr4mIJAF6vR69Xs+f/vQnAoHAfHdH5BJGNAoiIkmAXC7npZde4uWXX8ZsNlNSUsKjjz7KsWPH5rtrIpcYovtIRCSJ8Pv97Ny5k7179/LOO+9w4MABnn/++YTQn4jIhUY0CiIiScydd97J9u3bEzLkIiIXGtF9JCKSxCxdupTh4eH57obIJYQYkioikgR0d3fz1a9+ldtvv50VK1ZgMBg4dOgQP/3pT7nuuuvmu3silxCiURARSQL0ej3r1q3j5z//ObW1tYRCIdLT07nrrrt49NFH57t7IpcQ4p6CiIiIiEgCcU9BRERERCSBaBRERERERBL8/xWsb4DmzWuqAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BS.mesh_plt()  # PDE method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PDE approach is the topic of the notebook **2.1**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec4'></a>\n",
    "## Binomial tree\n",
    "\n",
    "\n",
    "Of course I cannot forget about the Binomial model!\n",
    "This is a simple but very powerful numerical method!\n",
    "\n",
    "I expect you to be familiar with this model. If not, have a look at the [wiki page](https://en.wikipedia.org/wiki/Binomial_options_pricing_model). \n",
    "Although I said I expect you to know the model, I'm not expecting that you have already implemented it!     \n",
    "Therefore, here I present an efficient implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BS Tree Price:  13.269537371978052\n"
     ]
    }
   ],
   "source": [
    "N = 15000  # number of periods or number of time steps\n",
    "payoff = \"call\"  # payoff\n",
    "\n",
    "dT = float(T) / N  # Delta t\n",
    "u = np.exp(sig * np.sqrt(dT))  # up factor\n",
    "d = 1.0 / u  # down factor\n",
    "\n",
    "V = np.zeros(N + 1)  # initialize the price vector\n",
    "\n",
    "# price S_T at time T\n",
    "S_T = np.array([(S0 * u**j * d ** (N - j)) for j in range(N + 1)])\n",
    "\n",
    "a = np.exp(r * dT)  # risk free compounded return\n",
    "p = (a - d) / (u - d)  # risk neutral up probability\n",
    "q = 1.0 - p  # risk neutral down probability\n",
    "\n",
    "if payoff == \"call\":\n",
    "    V[:] = np.maximum(S_T - K, 0.0)\n",
    "else:\n",
    "    V[:] = np.maximum(K - S_T, 0.0)\n",
    "\n",
    "for i in range(N - 1, -1, -1):\n",
    "    # the price vector is overwritten at each step\n",
    "    V[:-1] = np.exp(-r * dT) * (p * V[1:] + q * V[:-1])\n",
    "\n",
    "print(\"BS Tree Price: \", V[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec5'></a>\n",
    "## Limits of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BS_sigma = partial(BS_pricer.BlackScholes, \"call\", S0, K, T, r)  # binding the function\n",
    "sigmas = np.linspace(0.01, 10, 1000)\n",
    "\n",
    "plt.plot(sigmas, BS_sigma(sigmas))\n",
    "plt.xlabel(\"sig\")\n",
    "plt.ylabel(\"price\")\n",
    "plt.title(\"Black-Scholes price as function of volatility\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The BS formula is an increasing function of the volatility.    \n",
    "However, for higher volatilities, the graph becomes almost flat!!\n",
    "\n",
    "We can conclude that the model is reliable for volatilities in the range $0 - 400\\%$.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
